# First-Principles Study of the Band Gap Structure of Oxygen-Passivated Silicon Nanonets

- Linhan Lin
^{1}, - DeXing Li
^{1}and - Jiayou Feng
^{1}Email author

**4**:409

**DOI: **10.1007/s11671-009-9259-0

© to the authors 2009

**Received: **2 November 2008

**Accepted: **19 January 2009

**Published: **6 February 2009

## Abstract

A net-like nanostructure of silicon named silicon nanonet was designed and oxygen atoms were used to passivate the dangling bonds. First-principles calculation based on density functional theory with the generalized gradient approximation (GGA) were carried out to investigate the energy band gap structure of this special structure. The calculation results show that the indirect–direct band gap transition occurs when the nanonets are properly designed. This band gap transition is dominated by the passivation bonds, porosities as well as pore array distributions. It is also proved that Si–O–Si is an effective passivation bond which can change the band gap structure of the nanonets. These results provide another way to achieve a practical silicon-based light source.

### Keywords

Silicon nanonets Oxygen-passivated First-principles calculation Direct band gap Porosity Pore array distribution## Introduction

Being the basic material of modern integrated circuit technology for decades, silicon is one of the most important semiconductor materials. Due to its indirect band gap structure, the applications of silicon in optoelectronics are still limited. Nowadays, semiconductors with nanoscale structures are of great interest. It is believed that silicon will develop a direct band gap in nanoscale structures. A number of attempts such as porous silicon [1–3], silicon nanocrystals [4, 5], and silicon nanowires [6, 7] have been carried out to eliminate the obstacle. Other attempts such as Si/SiO_{2} superlattices structure [8, 9], Si/Ge quantum cascade [10], erbium-doped silicon-rich silicon oxide [11, 12], and all-silicon Raman laser [13] are also employed to achieve this luminescent transition. However, the practical silicon-based light source is still out of reach. A new silicon-based structure which is named silicon nanonet is presented in our study. It is a net-like structure constructed by drilling nanopore arrays along a special direction. The depths of the pores are of macroscale while the pore diameters and the pore walls are of nanoscale. It is found that the band structure of the nanonets changes from indirect to direct band gap when proper designs are provided.

## Calculation Details

The calculations of energy band structure of the silicon nanonets were based on the local density approximation and density function theory (LDA–DFT). The generalized gradient approximation (GGA), for the exchange and correlation effects [19] with the ultrasoft pseudopotentials [20] was selected for the calculations. These pseudopotentials require a quite low energy cut-off and guarantee good transferability and robustness. A geometry optimization of the silicon nanonets was carried out first with the atomic positions and the crystal cell parameters relaxed by total energy minimization. For the calculations of electronic characteristic, the cut-off energy of 340 eV was assumed in the plane-wave basis set, the SCF convergence tolerance of the electronic energy per atom was 1 × 10^{−6} eV and the k-point separation was 0.4 nm^{−1}.

## Results and Discussion

After the geometry optimization of the silicon nanonets, the atomic positions and the cell parameters become reasonable. The bond lengths are similar to the results reported in the study of siloxenic clusters [21]. As the length of Si–O bond is much smaller than the Si–Si bond, the distance between the silicon atoms which are linked by the same oxygen atom becomes much smaller in the Si–O–Si passivated nanonets. Hence, the presence of the oxygen atoms on the nanowalls of the Si–O–Si passivated nanonets produces a local diminution of the second-neighbor separation for silicon lattice, and consequently a structural contraction. For the –OH-passivated nanonet models, the Si–Si bond length increases in the case that both of the silicon atoms are linked with –OH, and decreases in the case that one silicon atom is linked with hydroxyl while the other with hydrogen. This is due to the different interactions between the passivation atoms.

In Fig. 2a, it is shown that the conduction band minimum (CBM) of bulk Si moves to 1/3 GZ or X due to the folding effect, which is in accordance with the theoretical analysis. In the 100X nanonets, the notable changes of the valence band occur at X. For the bulk Si, a valley exists at point X, which is much lower than G. With the porosity increases, the value of X increases and the valley disappears when the porosity reaches 29%. The G–X are 0.26, 0.08, 0.06, and 0.04 eV for bulk Si, 100X4B4W4P16O, 100X3B4W2P29O and 100X4B6W2P45O, respectively. However, G is always the valence band maximum (VBM) in all the 100X nanonets we concerned, which is the same with the location of VBM in bulk Si. In the conduction band, the changes of X are most important. With the porosity increases, the X–G changes from negative to positive and the CBM moves from X to G, leading to an indirect to direct band gap transition. All the 100X nanonets with porosities higher than 29% exhibit direct band gap structure in our calculation (Fig. 2c, d). For the 100D nanonets, it should be noted that the coordinate axes have been rotated a degree of 45° compared with the 100X nanonets. Thereby, the paths of ZAMGZRXG shown in the band structure of 100D nanonets correspond to ZRXGZAMG in the 100X nanonets. The location of CBM is fixed at M and the change of the M–G in the valence band is the key factor of the band gap transition. Our results show that the values of M–G are negative for 100D3B4W2P25O and 100D4B4W2P33O (Fig. 2e). However, when the porosity reaches 37%, the G–M becomes positive and the VBM moves from G to M and result in a direct band gap. Both the Si–O–Si passivated 100X and 100D nanonets exhibit the band gap transitions when the porosities are increased. However, the location of the VBM and CBM are different for these two models when direct band gap is obtained. Both the VBM and CBM locate at G for the 100X nanonets, while M for the 100D nanonets. This indicates that the distribution of the nanopore arrays is another key factor of the band gap structure of nanonets.

The 110X nanonets have the same macro appearance compared with the 100X nanonets, only with the difference of the crystal orientation of Si substrate. It should also be noted that a 45° rotation exists between the coordinate axes of the 110X nanonets and the 100X nanonets, which lead to the difference of the special points shown in the band structure. The motion of CBM appears in the GZ path. When the porosity is lower than 30%, the CBM stays at 1/6 GZ or 1/3 GZ (Fig. 2f). However, when the porosity increases to 39%, the CBM move from 1/6 GZ or 1/3 GZ to G (Fig. 2g). As the VBM always stays at X, the 110X nanonets exhibit indirect band gap in various porosities we study. The 110D nanonets can be treated as the 100X nanonets with the pore side orientation rotates a degree of 45°. Similar to the 110X nanonets, the 110D nanonets with different porosities in our study present indirect band gap with the CBM at point X and the VBM at point M (Fig. 2h). Both the –OH-passivated 110X and 110D nanonets have indirect band gap in different porosities, which is rather different from the results of 100X and 100D Si–O–Si passivated nanonets.

The pore wall width is the key factor in deciding the band gap of the nanonets. With the decreases of the pore wall width, the band gap increases due to the quantum confinement effect caused by the nanoscale of the pore walls. It should be noticed that the underestimation of the band gap induced by the approximation in the electron exchange-correlation energy in LDA–DFT method exists in this study without any correction.

*p*orbits in the Si–O–Si bond. The density of states (DOS) near the band edge of nanonets contributed by the oxygen atoms in Si–O–Si is larger than that of the hydrogen atoms in Si–H and the oxygen atoms in Si–OH. It is noted that the change of the band gap structure is not as obvious as that of the 110D nanonets shown in Fig. 3. This is because the number of the Si–O–Si bonds in the 110D3B4W2P13O is limited. In addition, the band gap is found to be in conjunction with the passivation bonds. The band gaps of 110D3B4W2P13H and 110D3B4W2P13OH are almost the same, 0.96 and 0.98 eV, respectively. However, it decreases to 0.86 eV for 110D3B4W2P13O, which may lead to the red shift in the photoluminescence spectrum.

## Conclusions

In summary, the structure design of oxygen-passivated silicon nanonets could result in indirect–direct band gap transitions of silicon. The Si–O–Si passivated 100X and 100D nanonets exhibit direct band gap characteristic when the porosities exceed 29 and 37%, respectively. The –OH-passivated 110D and 110X nanonets with different porosities we concerned in this study have indirect band gap. Si–O–Si bond has more effective influence on the band edge region of the nanonets than –H or –OH bonds and is expected to change the band gap structure of silicon nanonets. With the rapid development of the materials nano fabrication, it is expected that this electronic characteristic of the nanonets could be validated in experiments.

## Declarations

### Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 50571050), the National Basic Research Program of China (973 program, Grant No. 2007CB936601) and Tsinghua National Laboratory for Information Science and Technology of China.

## Authors’ Affiliations

## References

- Canham LT:
*Appl. Phys. Lett.*. 1990,**57:**1046. COI number [1:CAS:528:DyaK3cXmt1ahurc%3D]; Bibcode number [1990ApPhL..57.1046C] 10.1063/1.103561View Article - Canham LT, Leong WY, Beale MIJ, Cox TI, Taylor L:
*Appl. Phys. Lett.*. 1992,**61:**2563. COI number [1:CAS:528:DyaK38Xms1Srtb4%3D]; Bibcode number [1992ApPhL..61.2563C] 10.1063/1.108127View Article - Halimaoui A, Oules C, Bomchll G:
*Appl. Phys. Lett.*. 1991,**59:**304. COI number [1:CAS:528:DyaK3MXltVWqt78%3D]; Bibcode number [1991ApPhL..59..304H] 10.1063/1.105578View Article - Mutti P, Ghislotti G, Bertoni S, Bonoldi L:
*Appl. Phys. Lett.*. 1995,**66:**851. COI number [1:CAS:528:DyaK2MXjs1eitbg%3D]; Bibcode number [1995ApPhL..66..851M] 10.1063/1.113408View Article - Hill NA, Whaley KB:
*Phys. Rev. Lett.*. 1995,**75:**1130. COI number [1:CAS:528:DyaK2MXntlKntr4%3D]; Bibcode number [1995PhRvL..75.1130H] 10.1103/PhysRevLett.75.1130View Article - Sham TK, Nafter SJ, Kim P-SG, Sammynaiken R, Tang YH:
*Phys. Rev. B*. 2004,**70:**45313. Bibcode number [2004PhRvB..70d5313S] Bibcode number [2004PhRvB..70d5313S] 10.1103/PhysRevB.70.045313View Article - Brus L:
*J. Phys. Chem.*. 1994,**98:**3575. COI number [1:CAS:528:DyaK2cXit12qt74%3D] 10.1021/j100065a007View Article - Sullivan BT, Lockwood DJ, Labbé HJ, Lu Z-H:
*Appl. Phys. Lett.*. 1996,**69:**3149. COI number [1:CAS:528:DyaK28XnsVKks7g%3D]; Bibcode number [1996ApPhL..69.3149S] 10.1063/1.116811View Article - Lu ZH, Lockwood DJ, Baribeau J-M:
*Nature*. 1995,**378:**258. COI number [1:CAS:528:DyaK2MXpsVylsLY%3D]; Bibcode number [1995Natur.378..258L] 10.1038/378258a0View Article - Diehl L, Mentese S, Müller E, Grützmacher D, Sigg H:
*Appl. Phys. Lett.*. 2002,**81:**4700. COI number [1:CAS:528:DC%2BD38XpsFCitL8%3D]; Bibcode number [2002ApPhL..81.4700D] 10.1063/1.1528729View Article - Han HS, Seo SY, Shin JH:
*J. Appl. Phys.*. 2000,**88:**2160. COI number [1:CAS:528:DC%2BD3cXltFygsrc%3D]; Bibcode number [2000JAP....88.2160H] 10.1063/1.1304838View Article - Shin JH, Seo SY:
*Appl. Phys. Lett.*. 2000,**76:**1999. COI number [1:CAS:528:DC%2BD3cXitlSktbc%3D]; Bibcode number [2000ApPhL..76.1999S] 10.1063/1.126234View Article - Rong H, Liu A, Jones R, Cohen O:
*Nature*. 2005,**433:**292. COI number [1:CAS:528:DC%2BD2MXlt1KrsQ%3D%3D]; Bibcode number [2005Natur.433..292R] 10.1038/nature03273View Article - Ogata YH, Tsuboi T, Sakka T, Naito S:
*J. Porous Mater.*. 2000,**7:**63. COI number [1:CAS:528:DC%2BD3cXpvFyntA%3D%3D] 10.1023/A:1009694608199View Article - Mattei G, Valentini V, Yakovlev VA:
*Surf. Sci.*. 2002,**2002**(502):58. 10.1016/S0039-6028(01)01898-2View Article - Boukherroub R, Wayner DDM, Lockwood DJ:
*Appl. Phys. Lett.*. 2002,**81:**601. COI number [1:CAS:528:DC%2BD38XlsVamsbY%3D]; Bibcode number [2002ApPhL..81..601B] 10.1063/1.1492306View Article - Salonen J, Lehot VP, Laine E:
*Appl. Phys. Lett.*. 1997,**70:**637. COI number [1:CAS:528:DyaK2sXhtF2lu7g%3D]; Bibcode number [1997ApPhL..70..637S] 10.1063/1.118294View Article - Gelloz B, Kojima A, Koshida N:
*Appl. Phys. Lett.*. 2005,**87:**031107. Bibcode number [2005ApPhL..87c1107G] Bibcode number [2005ApPhL..87c1107G] 10.1063/1.2001136View Article - Perdew JP, Chevary JA, Vosko SH, Jackson KA:
*Phys. Rev. B*. 1992,**46:**6671. COI number [1:CAS:528:DyaK38XlvFyks7c%3D]; Bibcode number [1992PhRvB..46.6671P] 10.1103/PhysRevB.46.6671View Article - Vanderbilt D:
*Phys. Rev. B*. 1990,**41:**7892. Bibcode number [1990PhRvB..41.7892V] Bibcode number [1990PhRvB..41.7892V] 10.1103/PhysRevB.41.7892View Article - Pederson MR, Pickett WE:
*Phys. Rev. B*. 1993,**48:**17400. COI number [1:CAS:528:DyaK2cXhtFOisb4%3D]; Bibcode number [1993PhRvB..4817400P] 10.1103/PhysRevB.48.17400View Article