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 , 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 , and silicon nanowires   have been carried out to eliminate the obstacle . other attempts such as si / sio2 superlattices structure , si / ge quantum cascade , erbium - doped silicon - rich silicon oxide , and all - silicon raman laser   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 . it will be replaced by si  o bond , which is a stable state on the silicon surface . o passivation is also easy to achieve by exposing the sample in the air , electrochemical oxidation , or thermal oxidation   and has already been introduced into the microelectronics devices . it has also been widely studied in order to improve the luminescence property of porous silicon . for the 100 nanonets , most of the silicon atoms on the pore walls have two dangling bonds . we use oxygen - bridge to link neighboring silicon atoms in sides and hydrogen atoms to passivate silicon atoms in corners ( fig . therefore , hydroxyl is used for passivation and the si atoms in the corners are also passivated by h in order to reduce the internal stress ( fig . the special points in the reciprocal space of the nanonets and the paths in our calculation are shown in fig . the coordinate axes in the reciprocal space are established corresponding to the axes of the real space shown in fig . schematic view ofa100x4b5w3p29o , b100d5b5w2p29o , c110d4b6w2p20oh.d110x4b6w2p20oh , andespecial points in the reciprocal space of nanonets . for ( a)(d ) , 100 or 110 represents the orientations of the pore sides , xi or di depends on the shapes and the sizes of the primitive cell of the silicon nanonets , bj indicates the bore diameters of the nanopore , wk is the minimal widths of the nanowall , pn means the porosities of the silicon nanonets . oh means the nanowalls are oh - passivated , while o indicates the nanowalls are passivated by si  o  si . the crystal orientations of the primitive cells of the 100d and 110x nanonets have a 45 rotation compared with the other two models : thexandy - axis of 100x and 110d are , while   for 110x and 110d 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   with the ultrasoft pseudopotentials 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 ev and the k - point separation was 0.4 nm . 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 . as the length of 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 . figure 2shows the band structures of si and some nanonets constructed with 4  4  1 supercell . si exhibits a typical indirect band gap . however , when the nanopore arrays are introduced in the silicon supercell , both the conduction band and the valence band are significantly changed . energy band gap structure of bulk silicon and nanonets with the same cell size : 4  4  1 supercell.abulk si ( vbm : g , cbm : 1/3gz , eg : 0.71 ev),b100xb4w4p16o ( vbm : g , cbm : x , eg : 0.74 ev),c100x4b5w3p29o ( vbm : g , cbm : g , eg : 0.49 ev),d100x4b6w2p45o ( vbm : g , cbm : g , eg : 0.32 ev),e100d4b4w2p33o ( vbm : g , cbm : m , eg : 0.90 ev),f110x4b4w4p14oh ( vbm : x cbm : 1/6 gz or 1/3 gz eg : 0.94 ev),g110x4b6w2p39oh ( vbm : x , cbm : g , eg : 1.07 ev),h110d4b6w2p20oh ( vbm : m , cbm : x , eg : 0.90 ev ) 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 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 . when the porosity is lower than 30% , the cbm stays at 1/6 gz or 1/3 gz ( fig . however , when the porosity increases to 39% , the cbm move from 1/6 gz or 1/3 gz to g ( fig . 2 g ) . 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 . 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 it is shown that nanonets with the nanopore array distributions of 100x and 100d exhibit direct band gap characteristic when the porosity exceeds a special value . however , the passivation bonds can also lead to the changes of the band gap structure . in order to confirm our arguments , the band gap structure of 100d nanonets with different passivation conditions the cbm of 100d5b5w2p37h , all the dangling bonds on the nanowalls of which are passivated by h , stays at point g. however , the xg path in the valence band is almost horizontal , which indicates that the electrons on the corresponding state act as a two - dimensional electron gas in the real space ( fig . o  si , both the vbm and the cbm move to m and result in a direct band gap ( fig . the value of the band gap is also reduced due to the si  o  si passivation bonds . for further study of the effect of the different passivation bonds , the band structures of 110d nanonets with the same nanopore structure but passivated by h , oh , and si  o , 110d3b4w2p13h has an indirect band gap with the vbm at m and cbm at x , which is almost the same with 110d3b4w2p13oh . o  si , both the cbm and vbm move to point g and a direct band gap structure is obtained . o  si bond is an effective passivation bond which has greater influence on the band edge of nanonets , compared with the h and oh - passivated nanonets . it is due to the contribution of the electrons on the o-2porbits in the si  o  si bond . the density of states ( dos ) near the band edge of nanonets contributed by 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 . 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 . band gap structure ofa100d5b5w2p37h ( vbm : x or g , cbm : g , eg : 1.28 ev),b100d5b5w2p37o ( vbm : m , cbm : m , eg : 0.59 ev ) band gap structure of silicon nanonets with the same parameters but different passivation conditionsa110d3b4w2p13h ( vbm : m or g , cbm : x , eg : 0.96 ev),b110d3b4w2p13oh ( vbm : m , cbm : x , eg : 0.98 ev),c110d3b4w2p13o ( vbm : g , cbm : g , eg : 0.86 ev ) 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 . 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 . 50571050 ) , the national basic research program of china ( 973 program , grant no .
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 .