Properties of Si Nanostructural Modification on Si (111) Surface

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Properties of Si Nanostructural Modification on Si (111) Surface Yue-Hang Dong , Xiang-Ping Ding , Qing-Jun Zang , Wan-Sheng Su , Wen-Cai Lu PII: DOI: Reference:

S0577-9073(19)31011-1 https://doi.org/10.1016/j.cjph.2019.12.010 CJPH 1033

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Chinese Journal of Physics

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20 October 2019 29 November 2019 10 December 2019

Please cite this article as: Yue-Hang Dong , Xiang-Ping Ding , Qing-Jun Zang , Wan-Sheng Su , Wen-Cai Lu , Properties of Si Nanostructural Modification on Si (111) Surface, Chinese Journal of Physics (2019), doi: https://doi.org/10.1016/j.cjph.2019.12.010

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Highlights   

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Self-designed Si-NSs on Si (111) surfaces The designed Si-NSs modifications can enhance the optical absorption for Si surface Si surface with adsorbed Si-NSs are expected to have better optical absorption than the epitaxial grown ones Increase ratios of optical absorption differed at different wavelength range

Properties of Si Nanostructural Modification on Si (111) Surface

Yue-Hang Donga,b, Xiang-Ping Dingc, Qing-Jun Zangc, Wan-Sheng Sud,e,f,*, Wen-Cai Lua,c,*

a. Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin 130021, P. R. China b. School of Data Science and Software Engineering, Qingdao University, Qingdao, Shandong 266071, P. R. China c. College of Physics, Qingdao University, Qingdao, Shandong 266071, P. R. China d. National Taiwan Science Education Center, Taipei 11165, Taiwan e. Department of Electro-Optical Engineering, National Taipei University of Technology, Taipei 10608, Taiwan f. National Applied Research Laboratories, Taiwan Semiconductor Research Institute, Hsinchu 30078, Taiwan

*

[email protected]

*

[email protected]

Abstract Si nanostructures (Si-NSs) epitaxially grown or adsorbed on Si (111) surface, with various shapes including pit-like, bars, islands, hill-like, diamond-like and double cage, were studied theoretically using density-functional theory (DFT) calculations. The electronic and optical properties of these Si-NSs were calculated, showing that the designed Si-NSs modifications can enhance the optical absorption for Si surface.

Keywords: Si nanostructures; Si (111) surface; optical absorption

Graphical abstract

We designed more than 60 Si-NSs that modified onto the Si (111) surface and studied their structural, electronic and optical properties.

Introduction

Silicon is an important indirect-bandgap semiconductor, which has low electron-hole recombination efficiency. There are different shapes of Si nanostructures (Si-NSs) including nanowires, nanocrystals and quantum dots (QD) and so on. As is well known, silicon material plays a key role in semiconductor industry and solar cell materials, and its photoelectric conversion efficiency is higher than most of other solar cell materials. By using a reactive sputtering approach, small crystalline silicon particles surrounded with hydrogen atoms were fabricated, and both the experimental measurements and simplified calculation in Furukawa’s work supported that this material has an optical bandgap up to 2.4 eV, about two times that of Si diamond structure, and the author suggested this can be explained by a three-dimensional quantum-well effect in the small particles.1 Hao et al.2 fabricated the solar cell materials with the phosphorus-doped Si QDs covered by a SiO2 matrix that deposited on p-type crystalline Si substrates, and the open-circuit voltage was found to increase proportionally with reductions in QD size. In addition, Conibeer et al. reported a material for tandem photovoltaic cells based on Si QD.3 Kim et al.4 studied the electrical and optical properties of Si nanocrystal solar cells, showing that the optical absorption coefficient of quantum dots is about 14 times of the bulk Si. Recently, the optical absorptions of P-doped Si quantum dots were reported,5,6 which were shown to have a special plasma effect in optical absorption characteristics.

There were various methods in experiments to prepare the Si-NSs of different shapes. Nishimoto et al. and Vallejo et al. investigated experimentally the texturization of monocrystalline silicon, forming pyramidal nanostructures etched by sodium carbonate.7,8 Sanduijav et al. studied experimentally the epitaxial growth of Si QDs on pit-patterned Si (001) substrate, in which pits were filled to form inverted pyramid-like or multi-facetted dome-like quantum dots.9 Ogino et al. used a scanning probe microscope (SPM) instrument to carve grooves at different depths and to generate spatial point-like structures along the Si (110) direction.10 Laser interferometric lithography was used in their work to form pit structures on Si surface and such modifications on Si surface were found to be effective in reducing optical reflection.

Besides, many Si-NSs can be obtained from sophisticated prepared silicon oxides or nitrides. Si QDs can nucleate on Si3N4, SiO2, and SiOxNy by using SiH4 low-pressure chemical vapor deposition.11 The Si-NSs were produced by thermal annealing of SiOx films which prepared with a special vapor deposition,12 which is an effective way to synthesize Si-NSs and being further investigated.13 Yu et al. formed silicon nanoislands on a single crystalline silicon substrate by thermal annealing of silicon-rich oxide deposited by chemical vapor deposition, and this technique can be utilized to generate a high density of silicon nano-islands on Si substrate.14 Accordingly, reports for the formation of amorphous Si QDs grown in silicon nitride film, instead of SiOx film, but also prepared by plasma enhanced chemical vapor deposition.15

However, when exploring Si-NSs’ special electronic and optical properties, theoretically studied Si-NSs were generally much smaller than the experimental reported ones in size due to large computational cost. In 1997, Chelikowsky et al., using the real-space LDA approach, calculated Si nanoclusters with about 300~500 Si atoms, based on the most advanced supercomputer at that time.16 In another study, to deal with the large system, an empirical model that adopted a sophisticated potential was applied by Al-Douri et al.17 Meanwhile, for small systems, first principles calculation studies on free-standing Si nanoclusters18–21 and amorphous silicon QDs22 including their optical properties,17,23 were reported. In Refs. 18, 19 and 20, Si nanostructures contained about 70 to about 220 atoms were studied using DFT calculations. Ref. 20 adopted a 3c-TB method to perform optimization before DFT calculation due to the large scale of the structures. The Si clusters in Ref. 19 contained the same atom number as the stand-alone Si-NSs we designed. In this work, various Si172 Si-NSs with different shapes were prepared upon the Si (111) surface, and the modified surface were calculated firstly with DFTB+ code. Then, a dozen of candidate structures resulted from former step were further optimized with DFT method and followed by the analysis of the electronic and optical properties.

Computational Method At first, a fast calculation method DFTB+24 was used to verify and pre-optimize the designed and referenced Si-NSs (including the surface). According to the results, we

sorted out a dozen of candidate structures with lower energies to the further optimize using DFT calculations with the CASTEP module implemented in Materials Studio package,25 using the Perdew Burke Ernzerhof (PBE) functional, ultrasoft pseudopotential and a plane wave basis with the cutoff energy of 180 eV. Optical properties were analyzed by calculating dielectric values with the CASTEP module.

As is well known, the DFT method usually underestimates bandgaps, thus a scissors factor was applied here to adjust the underestimated bandgap. The Si diamond band gap was calculated to be 0.65 eV at the DFT-PBE level, which is 0.47 eV smaller than the experimental value of 1.12 eV, hence, we set a scissors factor of 0.47 eV. We carried out a test calculation from which the calculated optical absorption of Si diamond structure was in good agreement with the experimental data.26

Table 1. PBE and DFTB+ energies (in eV), and PBE binding energies (in eV) of the Si-NSs modified surfaces. Nanostructure

Type

PBE

DFTB+

Eb

Grown a1

diamond pit

-46856.47

-16557.95

136.16

a2

circular pit

-46851.94

-16560.02

111.66

b1

2-wrinkled layer grating

-46851.44

-16556.33

112.99

b2

3-wrinkled layer grating

-46836.59

-16552.28

103.13

c1

hexagonal island

-46834.52

-16549.87

105.24

c2

triangle island

-46810.98

-16496.54

78.76

d1

3-wrinkled layer cylinder

-46828.25

-16528.60

91.29

d2

4-wrinkled layer cylinder

-46819.09

-16510.69

88.41

e

Island

-46833.07

-16524.87

98.31

f

amorphous sphere

-46809.50

-16495.03

76.20

g

diamond-core

-46804.59

-16490.95

17.12

h

double-cage

-46804.24

-16492.61

50.52

Adsorbed

Figure 1. DFT-PBE optimized Si-NSs on the Si (111) surface.

Results and discussion

1. Structural Models Various shapes of Si-NSs were designed or from reference from Ref. 19, and then were introduced onto a Si (111) surface. The surface model consisted of 2-wrinkled layers of 8×8 Si (111) units with a lattice constant a0 = 5.485 Å, which was the DFT-PBE optimized lattice constant for the Si diamond phase. The Si atoms of the

bottom layer and the saturated H atoms were fixed in structural optimization. The vacuum space was kept larger than 10 Å. The designed Si (111) surface and the on-top Si172 nanostructure totally have as much as 428 Si atoms and 64 H atoms. The binding energies of the 12 low-energy candidate nanostructures resulted from pre-screening with DFTB+ and further optimizations with DFT were given in Table 1 and shown in Figure 1. To be noted that 9 of these 12 structures were self-designed and 3 of them were from Ref. 19.

We first designed several epitaxial grown pit-like structures. Their radiuses are around ~10 Å and their depths are ~7.1 Å. We managed the pits with different shapes including hexagonal, rectangular, triangular and diamond pits. The diamond pit-like structure, as shown in Figure 1(a1), has a top side length of ~20 Å and a bottom side length of ~14 Å. Figure 1(a2) shows a hexagonal pit-like structure, its side lengths are ~11 Å. Another diamond pit-like structure was also designed but not shown due to its higher energy, its side lengths are about 18 Å and the depth is ~9.5 Å. There are other pit-like structures with higher energies, like rectangular and triangle pits, their side lengths are ~22.4 Å x 7.7 Å (rectangular) and 23.4 Å (triangle).

Secondly, we designed slot-like Si-NSs. Figure 1(b1) is a 2-wrinkled layer structure with trapezoid gratings along direction [0 1 -1], each grating is about 9.5 Å high and the top and bottom side lengths are about 15.5 and 6.4 Å, respectively. Another designed trapezoid grating with a deeper grating depth about 11.9 Å was higher

in energy. Figure 1(b2) is a V-type groove that peeled along direction [0 1 -1]. The V-type groove is about 9.5 Å deep, and the top and bottom side lengths are about 22 and 15 Å, respectively. Another trapezoid V-type groove not shown in the figure with the top and bottom lengths of about 23 and 19 Å and the groove depth of about 9.5 Å was also constructed but higher in energy.

The island-like Si-NSs were built, including a hexagonal hill like island that was epitaxially grown on Si (111) surface (Figure 1(c1)). It consisted of 3-wrinkled Si layers (height of 11.9 Å), and its top and bottom layers are both Si (111) and its 6 sides are alternating (111) and (100) facets. There are other designed epitaxially grown Si islands including a triangle island with a side length of around 22.4 Å and a height of about 11.9 Å as shown in Figure 1(c2), and a rectangular island with a length of around 20 Å, a width of 13.4 Å and a height of 9.5 Å. Besides, cylinder-like Si-NSs with a height of about 9.5 Å, radius of 10 Å, and another one with a height of about 11.9 Å, radius of 9 Å were designed and shown in Figures 1(d1) and (d2).

We also introduced 4 adsorbed Si178 nanoclusters on Si(111) surface, as shown in Figures 1€, (f), (g), and (h). As mentioned above, the on-top Si172 structures (without the surface) (Figures 1(f), (g) and (h)) are from Ref. 19. The diamond-core Si172 nanocluster is the lowest-energy structure, followed by the double-cage, the amorphous sphere, and a bulk-like one. While in this work, when adsorbed on the Si (111) surface, the DFT calculated results showed that the amorphous Si172 cage (Figure 1(f)) was the lowest

energy one, followed by the diamond-core (Figure 1(g)) and then the double cage (Figure 1(h)). Moreover, a hexagonal island (Figure 1(e)) designed in this work, similar to the epitaxially grown one (Figure 1(c1)), is more stable than other adsorbed Si-NSs mentioned above. This hexagonal island has 3-wrinkled Si layers, with a radius of ~11 Å and a height of ~9.5 Å. Its top and bottom faces are (111) facets and the 6 side faces are alternating (111) and (100) facets.

The calculated results show that, among these nanostructures with different shapes, the epitaxial grown pit-like, grating and groove structures are relatively more stable, followed by the grown hexagonal island and the adsorbed hexagonal islands.

2. Optical Properties

In order to examine the influence of the surface thickness to the optical absorption, different thicknesses of the surfaces were considered. The Si surfaces with 2, 4, 6, 8, 10, 12 and 14 wrinkled layers were modeled and optimized by the DFT-PBE method, with a cutoff energy of 180 eV and a k-point mesh of 7×7×1. The optical absorptions were calculated with a scissors factor (0.47 eV) which acted as an energy gap correction. Obviously, in Figure 2, when the Si substrate reaches 14 Si wrinkled layers, the calculated optical absorption can be considered to be converged. Meanwhile, one can note that the optical absorption peak (42.4) of a 14-wrinkled layer surface is about 6 times larger than that of a 2-wrinkled layer surface (7.1). Therefore, to rationally reduce

the cost of computational resource and meanwhile considered the influence of surface thickness, the DFT results of optical absorption were corrected by multiplying 6.0.

Figure 2. Calculated dielectric coefficient’s imaginary part (i) of the pure Si (111) surface that modeled of different thickness, from 2- to 14-wrinkled layers. The peaks become closer when the surface getting thicker, and the value merely changes when the thickness reaches 14 layers.

Figure 3. Calculated imaginary part (i) of dielectric coefficient for (a1) grown diamond pit, (b1) grown 2-wrinkled layer grating, (c1) grown hexagonal island, (d1) grown 3-wrinkled layer cylinder, (e) adsorbed island, (f) adsorbed amorphous sphere, (g) adsorbed diamond-core, and (h) adsorbed double-cage nanostructures on the Si (111) surface.

Optical absorptions of the modified surfaces were estimated by their imaginary part of dielectric function that calculated using the CASTEP. Figure 3 shows the calculated imaginary parts of the dielectric function for these nanostructural modified surfaces. It can be seen that, regardless of the different shapes, the optical absorptions of the modified surfaces have all been enhanced and possess quite similar peaks, except that the 2-wrinkled layer grating shows an obviously higher absorption peak than the others. By comparing to the black curve which represents the pure Si surface (without

surface modification), other optical absorption peaks of the modified surfaces were considerably increased, but the peaks are all located near 300 nm with no obvious shifts.

For better comparing the increasing ratio of optical absorptions, we accumulated the optical absorption values at 0-380 nm (near ultraviolet region), 380-760 nm (visible light region), and 760-1000 nm (infrared), respectively. By the formula (Isurf&nanostruct Isurf) / Isurf, where Isurf&nanostruct and Isurf stand for the integrals of optical absorptions of the Si-NSs (including the surface) and the pure Si (111) surface respectively, Figure 4(a) gives the optical absorption enhancement ratio I/Isurf for all regions, Figure 4(b), (c) and (d) are the results for the different regions. For the visible region (380-760 nm) in Figure 4(b), the I/Isurf of the adsorbed spherical nanostructures of double-cage (column 8) (2.86), diamond-core (column 7) (2.73) and amorphous sphere (column 6) (2.65) are obviously larger than the epitaxially grown ones. For the infrared region (760-1000 nm), Figure 4(c) shows that the adsorbed nanostructures have better light absorption than the epitaxially grown nanostructures. In addition, all the I/Isurf are generally larger than 4 in this region. It can be seen from Figure 4(d) that all the structure’s I/Isurf are less than 1.0 in the ultraviolet region (0-380 nm), in which the grown 2-wrinkled layer grating has the highest value (0.92) which is obviously larger than the others (0.6 ~ 0.7). We can also note from Figure 4 that the enhancement rate of the optical absorption is more favorable at the infrared region, then less in the visible region and ultraviolet region.

Figure 4. Increase ratios of optical absorption ((Isurf&nanostruct - Isurface) / Isurface) at the different range of wavelength for the designed Si-NSs (modified on surfaces). Inner panel (a) is the increase ratio for the total wavelength from 0 to 1000nm, (b) is for visible region, (c) for infrared region, (d) ultraviolet region. In each inner panel, the Si-NS (a1) grown diamond pit, (b1) grown 2-wrinkled layer grating, (c1) grown hexagonal island, (d1) grown 3-wrinkled layer cylinder, (e) adsorbed island, (f) adsorbed amorphous sphere, (g) adsorbed diamond-core, and (h) adsorbed double-cage, are represented as column number 1 to 8 respectively.

3. Density of States For the electronic properties of these Si-NSs, the total and local DOSs were calculated. The total DOS (TDOS) and partial DOS (PDOS) of the pure Si (111) surface model are shown in Figure 5, and those of the Si-NS modified surfaces are given in

Figure 6. Although the total DOS behaviors of these nanostructures are quite similar to each other, we can still see small differences from the partial DOS curves in figures, especially the curves of surface’s first layer and that of the Si-NSs. The electronic states near the Fermi level are mainly contributed by the 3p states of silicon atoms from the Si-NS and surface’s top layer, indicating that Si 3p electrons are obviously much easier to be excited compared to Si 3s electrons. It can be also seen that the valence bands consist of Si 3s, hybrid Si 3s and 3p, and Si 3p states, from lower to higher energy region.

Figure 5. Total and partial DOS of a standalone Si (111) surface (2-wrinkled layer) saturated by H atoms at the bottom. The surface model, including the H atoms, totally have 5 atom layers, thus the partial DOS are given for each atom layer.

Figure 6. Total and partial DOS for the designed Si-NSs (with surfaces) (a1) grown diamond pit, (b1) grown 2-wrinkled layer grating, (c1) grown hexagonal island, (d1) grown 3-wrinkled layer cylinder, (e) adsorbed island, (f) adsorbed amorphous sphere, (g) adsorbed diamond-core, and (h) adsorbed double-cage. The surfaces consist of 4 atom layers (2-wrinkled layers), thus, except the total DOS, partial DOS for each atom layer of the surface are shown. In each panel, ordered from top to bottom, there are 7 inner figures which the total DOS for the modified surface, partial DOS for stand-alone Si-NS, partial DOS for the first, second, third and the fourth atom layer of the surface and the partial DOS for H atoms.

Conclusions

Si (111) surface modified by epitaxially grown and adsorbed Si-NSs were studied using the DFTB+ code and DFT methods. The stability order of the Si-NSs is pit-like > nanobar > nanoisland > adsorbed ones. The calculated DOSs of the on-surface nanostructures show that their valence band electrons around the Fermi level are composed of Si 3p states from the Si atoms of the surface’s top layer and the nanostructures. Based on optical analysis results using CASTEP module, the adsorbed nanostructures on the Si surface can considerably enhance optical absorption, and the positions of the main absorption peaks did not have obvious shifts. With the surface modifications, all the systems displayed increased optical absorptions in the infrared and visible wavelength regions, and within these two regions, the Si surface with adsorbed Si-NSs are expected to have better optical absorption. While in the ultraviolet region, most increasing rates of the Si-NS’s absorption are close and relatively smaller than those of longer wavelength regions.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 21773132 and 21273122). W. –S. Su would like to thank the Ministry of Science and Technology of Taiwan for financially supporting this research under Contract No. MOST 108-2112-M-979-001. Support from the National Centers for Theoretical Sciences and High-performance Computing of Taiwan in providing huge computing resources to facilitate this research are also gratefully acknowledged.

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