Experimental section

We prepared three different types of Si NCs in Si-rich oxide (SRO) films with different SiO _x compositions and doping levels as summarized in Table I. Samples (a) and (b) with a composition of SiO_1.5 (40 at.% Si in SRO) were fabricated by a co-sputtering method using Si, SiO₂, P₂O₅, or B₂O₃. Sample (c) with a composition of SiO_0.93N_0.22 (52 at.% Si in SRO) was fabricated by plasma-enhanced chemical vapor deposition. Samples (d) and (e) with a composition of SiO_0.37 (73 at.% Si in SRO) were fabricated by a sputtering method. The film structure of samples (c)–(e) was multilayers of P- or B-doped SRO and SiO₂. All samples were annealed at 1100–1150 °C for 30 min–1 h in N₂ to form Si NCs. A detailed explanation about sample preparation is described in previous reports.^[ Reference Fujii, Hayashi and Yamamoto ^{9 –} Reference Yang, Nomoto, Lin, Wu, Puthen-Veettil, Zhang, Jia, Conibeer and Perez-Wurfl ^{11 ]}

Table I.

Sample list prepared within this study.

SRO, silicon-rich oxide; P, phosphorus; B, boron.

For the preparation of APT measurements, sharp needle-shaped tips were prepared for each sample using an Auriga FIB-SEM (Zeiss). A few hundred nm of Pt was deposited onto the surface of the samples to protect the film from Ga ion damage and then milled using the standard lift-out procedure.^[ Reference Felfer, Alam, Ringer and Cairney ^{12 ]} The APT measurements were performed using a LEAP 4000XSi (CAMECA) system equipped with a pulsed UV laser (λ = 355 nm) and a detector efficiency of 0.57. The chamber pressure was within the range of 10⁻¹²–10⁻¹¹ Torr. The laser pulse energy and rate were 100 pJ and 250 kHz, respectively. The specimen holder was cooled to ~40 K. The APT data were then reconstructed using commercially available IVAS^™ software (version 3.6.6). Although the default image compression factor (1.65) and field factor (3.3) were used, the standard reconstruction algorithm in this work is volume conserving,^[ Reference Vurpillot, Gault, Geiser and Larson ^{13 ]} so the calculated size of Si NCs shown later should be fairly constant regardless of the reconstruction parameters used. The P or B distribution as well as the concentration were analyzed using a proximity histogram (proxigram).^[ Reference Hellman, Vandenbroucke, Rusing, Isheim and Seidman ^{14 ]}

Results and discussion

Figure 1 shows a 3D reconstruction of P- and B-doped Si NCs. The Si NCs interfaces can be qualitatively visualized using iso-concentration surfaces that create bounding volumes that contain at least 65 at.% Si. This was applied to all samples in the same manner. Figure parts of (a)–(e) are the same sample names of (a)–(e) as labeled in Table I. The 3D images show that the Si NCs of samples (a) and (b) were well separated from each other in 3D, despite the film being a single SRO layer fabricated by the co-sputtering method without a multilayered structure. We classify these types of Si NCs as “isolated Si NCs”. In sample (c) the use of NO₂ during deposition results into N incorporation of around 5 at.% in the SRO layer.^[ Reference Hartel, Hiller, Gutsch, Löper, Estradé, Peiró, Garrido and Zacharias ^{15 ]} It has been reported that introducing nitrogen inhibits Si diffusion,^[ Reference Mulloni, Bellutti and Vanzetti ^{16 ]} hence, the sample needs a slight increase in the annealing temperature (from 1100 °C to 1150 °C) to complete the crystallization of Si NCs.^[ Reference Hartel, Hiller, Gutsch, Löper, Estradé, Peiró, Garrido and Zacharias ^{15 ]} On the other hand, a phase separation of SiO _x and growth of Si precipitates during high-temperature annealing is thought to be very fast due to the out-diffusion of oxygen.^[ Reference Sarikov, Litovchenko, Lisovskyy, Maidanchuk and Zlobin ^{17 ]} In fact, a successful Si NCs formation has been demonstrated by rapid thermal annealing in a short time within a few seconds.^[ Reference Hiller, Gutsch, Hartel, Löper, Gebel and Zacharias ^{18 ]} Therefore, the influence of introducing nitrogen on the size and the distribution of Si NCs in sample (c) might be a minor issue. The Si NC distribution was similar to that of samples (a) and (b), but sample (c) had larger Si NCs and less SiO₂ matrix volume compared with samples (a) and (b). This should simply be because the excess Si content in sample (c) is higher than that in samples (a) and (b). On the other hand in samples (d) and (e), the Si NCs were more likely connected to each other. We classify this type of Si NCs as “connected Si NCs”. Recently, a threshold value from non-percolating to percolating network was reported in between SiO_0.5 and SiO_0.7,^[ Reference Laube, Gutsch, Wang, Zacharias and Hiller ^{19 ]} thus, “connected Si NCs” should be dominant for samples (d) and (e). (Please note that isolated Si NCs also exist in this type of “connected Si NCs”.) Although it was not possible to obtain sufficient crystallographic information for the reconstruction, high-resolution transmission electron microscopy and Raman results in previous works showed that the Si NCs fabricated in the same manner here were indeed crystallized as shown in Refs. Reference Fujii, Hayashi and Yamamoto9–Reference Yang, Nomoto, Lin, Wu, Puthen-Veettil, Zhang, Jia, Conibeer and Perez-Wurfl11.

Figure 1.

3D reconstructions of (a) P-doped Si NCs (SiO_1.5), (b) B-doped Si NCs (SiO_1.5), (c) P-doped Si NCs (SiO_0.93N_0.22), (d) P-doped Si NCs (SiO_0.37), and (e) B-doped Si NCs (SiO_0.37). The box sizes are (a) 53 × 53 × 130 nm³, (b) 61 × 61 × 156 nm³, (c) 71 × 71 × 145 nm³, (d) 44 × 44 × 167 nm³, and (e) 55 × 55 × 160 nm³.

For a quantitative analysis of the Si NCs size, we investigated the volume fraction and number density for all samples as shown in Fig. 2. The volume fraction was defined as the ratio of the Si NCs volume to the total reconstruction volume. The number density was calculated by dividing the number of Si NCs by the total volume. The trend clearly showed an increase in the volume fraction and a decrease in the number density as the excess Si content increased. This suggests that there are many small Si NCs in samples for lower Si content (samples (a)–(c)) and a small amount of large Si NCs in samples for higher Si content (samples (d) and (c)), as one might expect.

Figure 2.

Volume fraction and number density of P- and B-doped Si NCs in the oxide matrix.

The distribution of the P or B inside and outside of the Si NCs was studied by proxigram analysis as shown in Fig. 3. From the profile, it was found that P and B were incorporated into the Si NCs. For the amount of P incorporation, the P concentration seems to be close to, or even above, the solid solubility limit at ~1100 °C in bulk Si (around 2.4 at.% for P, 0.5–1.2 at.% for B).^[ Reference Trumbore ^{20 –} Reference Olesinski and Abbaschian ^{22 ]} This may indicate that the solid solubility limit of dopants in Si NCs could be different from that in the bulk Si.^[ Reference Sumida, Ninomiya, Fujii, Fujio, Hayashi, Kodama and Ohta ^{23 ]} In addition, there was a preferential location of P and B in the system of Si NCs/SiO₂. For example, P preferred to locate inside the Si NCs rather than the SiO₂ matrix. Again, the influence of nitrogen in sample (c) should be considered, but the profiles between sample (a) and (c) were close enough to claim the preferential location of P. On the other hand, B tended to be located in the matrix region and the B concentration gradually decreased toward the Si NCs core. The profile in Fig. 3(c) were slightly different from Fig 3(a) and (b). The proxigram analysis might be affected by neighboring Si NCs, which are randomly connected to each other forming the complex shape and distribution. Further analysis is necessary to understand the distribution for the connected Si NCs. A pile-up or segregation of P and B was slightly observed around interface between Si NCs and the matrix. The diffusivities of P and B in Si and SiO₂ have been reported by many researchers.^[ Reference Ghezzo and Brown ^{24 ]} Although it is not straightforward to compare the diffusivity for all samples, Table II summarizes calculations of the diffusion length of P and B in Si and SiO₂ for all samples. In the case of the diffusion of P and B in Si, the pre-exponential diffusion coefficient, D₀, and the activation energy, Q, were extracted from the slope of the temperature versus diffusivity figures from experimental data; 3.85 cm²/s and 3.66 eV was calculated for P,^[ Reference Fair and Tsai ^{25 ]} and 3.17 cm²/s and 3.59 eV for B.^[ Reference Fair ^{26 ]} In the case of the diffusion of P and B in SiO₂, D₀, and Q were also extracted from the slope of the temperature versus diffusivity figures; for P they are 1.86 × 10⁻¹ cm²/s and 4.03 eV,^[ Reference Ghezzo and Brown ^{24 ]} and 3.16 × 10⁻⁴ cm²/s and 3.53 eV for B.^[ Reference Ghezzo and Brown ^{24 ]} The one order of magnitude difference in diffusion rates within Si and SiO₂ of both types of dopants might explain the enrichment at the interface between the Si NCs and the matrix after annealing. It is also proposed that the interface between Si NCs and SiO₂ has a high-interface energy (strain) due to lattice mismatches between Si NC and amorphous-SiO₂ matrix.^[ Reference Hadjisavvas and Kelires ^{27 ]} Our observation implies that dopants at the interface may release the strain as reported in the system of bulk Si/SiO₂.^[ Reference Sakamoto, Nishi, Ichikawa and Ushio ^{28 ]} This argument is supported by the fact that the P and B diffusion lengths in Si NCs system correlate with a difference in the length of the diffusion profiles, as mentioned above. This implies that there might be other factors that determine the location of dopants atoms that should motivate further studies.

Figure 3.

Proxigram analysis of P- and B-doped Si NCs in the oxide matrix. The composition of SRO is (a) SiO_1.5, (b) SiO_0.93N_0.22, and (c) SiO_0.37.

Table II.

Diffusion length of P and B in Si and SiO₂.

^a D₀ and Q: 3.85 cm²/s and 3.66 eV for P, and 3.17 cm²/s and 3.59 eV for B.

^b D₀ and Q: 1.86 × 10⁻¹ cm²/s and 4.03 eV for P, and 3.16 × 10⁻⁴ cm²/s and 3.53 eV for B.

Similar distribution behavior of P and B have been reported in P- and B-doped Si nanowires, suggesting a segregation behavior between P and B.^[ Reference Fukata, Ishida, Yokono, Takiguchi, Chen, Sekiguchi and Murakami ^{29 ]} As mentioned above, phase separation and Si precipitation occur in a very short time within a few seconds, so the distribution and size of Si NCs in the annealing condition here (1100–1150 °C 30 min–1 h) does not change significantly. Moreover, considering the feature size being analyzed here, the diffusion length of P and B in Si and SiO₂ in Table II is substantially longer to assume that the system is in equilibrium or close enough to the equilibrium conditions. In Fig. 4, we extracted the segregation coefficient (m) from the plot of the proxigram in Fig. 3 to study the different distribution behavior between P and B. The segregation coefficient is represented by the ratio of equilibrium concentration of impurity in the silicon to that in the oxide.^[ Reference Grove, Leistiko and Sah ^{30 ]} The P and B concentration in Si NCs and the oxide region was extracted from the distance around 0.5 m and −2.5 m, respectively. Although there was a slight deviation, both m values of P and B were consistent with the trend of the reference values, which was m > 1 for P and m < 1 for B.^[ Reference Grove, Leistiko and Sah ^{30 ]} Moreover, interestingly, the segregation coefficient for P and B was almost constant at least in the similar annealing conditions, even though the concentrations in Si NCs and the matrix were quite different as shown in Fig. 3. In other words, regardless of the amount of introduced impurity, the different P and B segregation coefficients are reflected in the dopant's incorporations into Si NCs and matrix, respectively.

Figure 4.

Extracted segregation coefficient of P- and B-doped Si NCs in the oxide matrix from the proxigram analysis.