Exceptional Optoelectronic Properties of Hydrogenated Bilayer Silicene

Bing Huang, Hui-Xiong Deng, Hoonkyung Lee, Mina Yoon, Bobby G. Sumpter, Feng Liu, Sean C. Smith, and Su-Huai Wei National Renewable Energy Laboratory, Golden, Colorado 80401, USA Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6493, USA State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Korea Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA (Received 25 November 2013; revised manuscript received 7 April 2014; published 19 May 2014)

Silicon is one of the most important building blocks in today's high-technology fields.For example, the majority of solar cells fabricated to date have been based on singlecrystalline or polycrystalline Si in a diamond structure, with a market share of greater than 90% [1].This is not only because Si is the second-most-abundant element on the Earth but also because the Si-based photovoltaic (PV) industry benefits from the mature Si-based microelectronics technology.However, although diamond Si has a fundamental (indirect) band gap of 1.12 eV [2], its optical (direct) gap is larger than 3 eV [3]; thus, Si is not a good absorber of sunlight [4].As a result, the Si absorber layer must be sufficiently thick (usually > 100 μm) to absorb enough visible light, and it must be assisted by phonons, which significantly increases the cost of Si-based PV modules [5].Because of this drawback, in the past several decades, significant effort has been devoted to the search of materials that have better absorption coefficients in the visible region.One approach is to identify different materials that can replace silicon for solar cells.For example, CdTe [6,7], CuðIn; GaÞSe 2 [8,9], and Cu 2 ZnSnðS; SeÞ 4 [10,11] based single-junction, thin-film solar cells have been widely studied in the past few decades because these absorbers have promising direct band gaps between 1 and 1.5 eV, which are expected to produce highefficiency solar cells according to the Shockley-Queisser criteria [12].Another approach would be to engineer the structural and electronic properties of silicon to improve its optical absorption.
Several specific approaches have been proposed to manipulate the band structure and optical property of silicon.The first method is to search metastable silicon phases with better optical coefficients in the visible region.For example, cubic Si 20 [13] and M-10 Si [14] are predicted to have quasidirect band gaps of 1.40 and 1.55 eV, respectively.However, the synthesis of these high-energy metastable silicon phases is still a challenge.The second method is to alloy Si with other common materials to obtain new functional materials.For example, alloying Si with AlP to form Si 3 AlP [15] can reduce the optical gap of Si to around 2.0 eV [16], which is much smaller than that of diamond Si but still higher than the optimal value for solarcell application; alloying Si with Ge on a proper substrate may form the magic superlattice structures such as α 12 Si-Ge with a dipole-allowed direct band gap of 0.61 eV [17,18], but experimental synthesis of this complex structure is difficult because of the interface strain.The third method is to design proper nanostructured silicon, but the dipole transitions at the band edges of silicon quantum dots are quite weak and depend strongly on the structures and surface passivations [19].These limitations encourage us to investigate new approaches to manipulate the electrical and optical properties of silicon materials for optoelectronic applications.
Low-dimensional materials themselves are usually not sufficient for various applications, and chemical functionalization can play an important role to further modify their electronic properties for various specific applications.Among numerous chemical methods, hydrogenation has been demonstrated to be one of the most powerful approaches to tune the electronic properties of 2D materials.For example, it has been demonstrated that hydrogenation can open sizable band gaps in graphene [40][41][42], graphyne [43], and single-layer silicene [44][45][46].However, none of these hydrogenated structures reported to date is suitable for solar applications; in particular, there may be a strong phase separation in the ground states of these materials.As a new silicon phase, it is quite interesting to study if the intrinsic and hydrogenated BS (HBS) could realize controllable optoelectronic properties for solar cells and other optical applications.
In this article, by employing first-principles calculations and the cluster-expansion approach, we have systemically studied the structural and electronic properties of intrinsic and hydrogenated BS.Our calculations demonstrate that BS is a strongly indirect semiconductor that is not suitable for optoelectronics.However, hydrogenation of BS can induce some well-ordered intermediate phases with unexpected electronic properties.At low hydrogen concentrations, four single-and double-sided HBS ground states have dipole-allowed direct (or quasidirect) band gaps with gaps between 1 and 1.5 eV, which are suitable for solar applications.Surprisingly, at high hydrogen concentrations, we discover three well-ordered double-sided HBS structures that have direct (or quasidirect) band gaps within the color range of red, green, and blue (RGB).The combination of RGB emitters can achieve a white lightemitting diode (LED), which has great potential for solidstate lighting.Thus, hydrogenation of BS can achieve new silicon-based solar absorbers, but it can also extend silicon to other optoelectronic applications such as white LEDs.
All the density-functional-theory (DFT) calculations are performed by using the VASP code [47].Projectoraugmented-wave (PAW) potentials are used to describe the core electrons, and the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional is selected in our calculations.The effect of van de Waals (vdW) interactions is taken into account by using the empirical correction scheme of Grimme (DFT þ D=PBE) [48], which has proved to be successful in describing various layered structures [49,50].The kinetic-energy cutoff for the plane-wave basis is set to 400 eV.A 15-Å vacuum layer is adopted to simulate isolated bilayer silicene.The Γ-centered k-point mesh with sufficient k-point density is used for the Brillouin-zone integration for all the structures.All the structures are fully relaxed until the force on each atom is less than 0.01 eV=Å.It is well known that normal DFT calculations usually underestimate the band gaps of semiconductors.Because hybrid functional calculations could give improved results for both conventional semiconductors and low-dimensional materials, we adopt the Heyd, Scuseria, and Ernzerhof (HSE06) hybrid functional [51] to calculate all the electronic structures of our studied systems.It has been shown that the HSE06 functional can describe the band gaps of new silicon phases very well, close to GW results [13,14].
To search the ground-state structures at different hydrogen concentrations, we treat HBS (SiH x ) as alloy systems, with each site either occupied by hydrogen or not, and we use the cluster-expansion (CE) method established in the alloy theory to describe the system.In the CE approach, the alloy Hamiltonian is mapped onto a generalized Ising Hamiltonian [52,53]: where the indices i, j, and k range over all occupation sites.S m ðσÞ is þ1 when it is occupied by H and −1 if it is not.Every cluster figure α is associated with an interaction parameter J α , which gives the contribution of the specific cluster figure to the properties.Generally, CE is able to represent any SiH x energy EðσÞ by an appropriate selection of J α , and then it can predict the absolute lowest-energy structures within certain atom supercells.The parameters of J α can be determined by fitting them to the first-principles energies of selected configurations [54].Initially, we put H atoms randomly on the top site of bilayer silicene to generate various alloy structures.The cross-validation (CV) score [54], obtained by a least-squares fit to firstprinciples energies, is used to measure the CE quality, and we have made sure that all the CE fittings in our study can reach a reasonably low CV score.
For the stacking of two single-layer silicene, there are generally two types of BS with high symmetry, i.e., AA and AB stacking.Because of the existence of buckling in the single-layer structure [22,46], the single-layer silicene can be divided into top and bottom Si layers.This nonplanar structure allows each AA and AB stacking to have two nonequivalent variants (top-top and top-down); i.e., there are four possible stacking structures with different symmetries: AA-1 (D 3d symmetry), AA-2 (D 3h symmetry), AB-1 (D 3d symmetry), and AB-2 (C 3v symmetry), as shown in Fig. 1(a).The formation energy E f of bilayer silicene with respect to single-layer silicene is defined as , where E BS and E S are the total energies (per unit cell) of bilayer and single-layer silicene, respectively.Obviously, all these bilayer structures have lower energies than that of single-layer silicene.In these four structures, AB-1 has the lowest energy, which is consistent with the conclusion from Liu et al. [35].However, our further investigation finds that the AA-1 and AA-2 structures are both metastable, and the most stable AA-stacking structure is AA-3 with D 6h symmetry [Fig.1(a)].For the structure of AA-3, the in-plane Si-Si bond length is stretched from an initial 2.25 Å to 2.39 Å, and the silicene layers become flat.At the same time, the interlayer Si-Si bond lengths are decreased to 2.42 Å, which means that all the Si atoms form interlayer bonds to fully realize sp 3 hybridization.As a result, the E f of the AA-3 structure is 24 meV=Si lower than that of AB-1.This conclusion does not change even when excluding the vdW corrections.Our finding is consistent with that from Tritsaris et al. [37] based on PBE calculations without vdW corrections.To further enhance our conclusion, we have performed global-minimum optimization using the particle-swarm-optimization (PSO) method [55] to confirm the proposed bilayer AA-3 structure as the global ground state.In this structure search, the hexagonal lattice of Si is not assumed.Instead, we generate random structures (both atomic coordinates and lattice parameters) to initialize the simulations.The population size is set to 20, and the number of generations is set to 20.The number of atoms is fixed to 4 Si=cell, and only bilayer structures are considered.After several generations, we have successfully confirmed that the AA-3 structure is indeed the most stable bilayer silicon phase.
It is important to check the stability of the bilayer AA-3 structure.First, the phonon spectrum of AA-3 is calculated by finite-different methods to understand its dynamic stability.As demonstrated in Fig. 1 stable.Second, first-principles molecular-dynamic simulations, using a Nose-Hoover thermostat with a time step of 2 fs, are performed to check the thermal stability of AA-3 at a finite temperature.A 5 × 5 100-atom AA-3 supercell is selected, as shown in the inset of Fig. 1(c).The fluctuation of the total energy as a function of simulation time at 600 K is plotted in Fig. 1(c).After 20 ps, no structural destruction of AA-3 is found, except for some thermal fluctuations, which demonstrates that freestanding AA-3 can stably exist (at least) at 600 K.This temperature is high enough for optoelectronic applications.Unfortunately, the calculated band structure [Fig.1(d)] shows that the bilayer AA-3 is a strongly indirect semiconductor.It has a minimum direct band gap of 1.6 eV (at the M point) and a fundamental band gap of 0.10 eV [a conduction-band minimum (CBM) at the M point and valence-band maximum (VBM) at the K-Γ line].We also note that the AA-3 structure shows metallic (negative band gap) behavior under conventional PBE calculations, indicating that hybrid functional calculations are quite necessary to correctly describe the electronic structures of BS-related materials.Although there are some experimentally measured band structures of BS on the Ag (111) surface, it is difficult to directly compare our theoretical results for freestanding BS to these experimental ones because the strong interactions between the Si and Ag (111) surface can largely modify the electronic structure of freestanding BS [27].Like bulk silicon, this kind of strongly indirect band structure is not suitable for solar and other optoelectronic applications.Thus, it is highly desirable to investigate the possibility of modifying this new silicon structure by hydrogenation.In the present article, we focus our study on freestanding BS.For the cases of stable configurations of BS on substrates, e.g., an Ag(111) substrate, some discussions are provided in Ref. [56].
In practice, hydrogen atoms can adsorb on either single or double sides of BS during hydrogenation, depending on the situations of hydrogenation [40][41][42].Thus, both singlesided and double-sided HBS are systemically studied.Because of the small size of H atoms, our calculations show that H atoms prefer to adsorb on the top of Si atoms, similar to hydrogenated graphene [40][41][42]57].For singlesided SiH x , the highest H concentration is x ¼ 0.5.In the structure of SiH 0.5 [inset of Fig. 2(a)], hydrogen-atom adsorption on the top basal plane of BS breaks the interlayer Si-Si bonds, which indicates that the strength of Si-H bonds is stronger than that of interlayer Si-Si bonds.After the interlayer bonds are broken, the in-plane Si-Si bond lengths are decreased to 2.32 Å, while the interlayer Si-Si bond lengths are increased to 3.34 Å, belonging to vdW interactions.For a single-sided SiH x with arbitrary configuration σðxÞ, its formation energy (E f ) is defined as where EðSiH 0 Þ and EðSiH 0.5 Þ are the energies of silicene and SiH 0.5 , respectively.We have calculated the E f of selected 80 SiH x structures, containing at most 42 atoms=unit cell, using first-principles methods.The CE Hamiltonian of SiH x is obtained by fitting to the 80 first-principles energies.The CV score of this CE fitting is 33 meV, indicating that the obtained CE Hamiltonian is accurate enough to predict the E f of all the SiH x structures.Then, the energies of all the symmetry-inequivalent SiH x alloys (> 10000) within 42 atoms=cell are calculated by the CE Hamiltonian, and the results are shown in Fig. 2(a).Interestingly, six intermediate ground states are discovered, as plotted in Fig. 3   (2.34Å) and bond angle (106°) at the distortion sites are close to those in bulk Si, which indicates that distortion can maximize the ideal sp 3 hybridization to lower the total energies.Generally, the hexagonal sublattice of silicene is kept during hydrogenation, which is significantly different from that of hydrogenated single-layer silicene [46] and consistent with the fact that BS is more stable than singlelayer silicene.
For double-sided SiH x , the highest H concentration is x ¼ 1, and its structure is shown in Fig. 2(b).The E f of double-sided SiH x with configuration σðxÞ is defined as where EðSiH 0 Þ and EðSiH 1 Þ are the energies of silicene and SiH 1 , respectively.The E f of a total of 72 alloy structures are calculated using first-principles methods and fitted by the CE Hamiltonian.The CV score for this CE fitting is 36 meV.Using this CE Hamiltonian, we have calculated all the E f of symmetry-inequivalent double-sided SiH x structures (> 10000) within 36 atoms/cell, as shown in Fig. 2(b).Surprisingly, six intermediate ground states are discovered at specific H concentrations, which are quite different from chemically functionalized double-sided graphene [57].Usually, there are no intermediate ground states in chemically functionalized freestanding 2 D materials with single-atom thickness because the existence of strong double-sided adsorbate-adsorbate interactions can give rise to the clustering of adsorbates [46,53,57].For double-sided HBS, the formation of the sp 3 bond on one side and the subsequent increase in the layer-layer distance significantly reduce the strength of the attraction of H on opposite sides.This explains why some intermediate ground states can form in double-sided HBS.As shown in Fig. 4, those structures are Si 16 H 4 (D 6h symmetry), Si 12 H 4 (D 2h symmetry), Si 8 H 4 (D 2h symmetry), Si 12 H 8 (D 2h symmetry), Si 16 H 12 (D 2h symmetry), and Si 12 H 10 (D 3h symmetry).In these six ground states, we find that H atoms prefer to symmetrically adsorb on the top and bottom sides of HBS, giving rise to relatively higher structural symmetry compared to single-sided HBS.Similar to single-sided SiH x , H adsorption breaks the underneath Si-Si bonds, and the local distortion of Si atoms can maximize the ideal sp 3 hybridization.Also, the average Si-Si bond length and bond angle at the distortion sites are close to those in single-sided HBS.The calculated average binding energy between H atoms and BS in these ground states is around 820 meV/H, close to the value between BS and the Ag(111) substrate, which indicates that hydrogenation plays a similar role as the Ag substrate to further stabilize the BS structures.Generally, the ground state of a single-or double-sided SiH x structure with an arbitrary concentration could be phase separated into its neighboring ground states.For example, the ground state of any double-sided SiH 0.4 structure can be the combination of Si 12 H 4 [x ¼ 1=3, Fig. 4(b)] and Si 8 H 4 [x ¼ 1=2, Fig. 4(c)] structures.This kind of phase separation is also experimentally observed in chemically functionalized graphene [58].
Because intrinsic BS is a strongly indirect-gap semiconductor, it is quite interesting to study the suitability of SiH x for optoelectronics.In Fig. 5, we have plotted the calculated band gaps of these single-sided and double-sided SiH x ground states as a functional of H concentration.For some special indirect band-gap semiconductors, if the gap differences between the indirect band gap and minimum direct band gap are less than 0.1 eV, we call them quasidirect gap semiconductors.Quasidirect band-gap systems may behave as direct band-gap systems in most optoelectronic applications [13,14,59].As shown in Fig. 5, we find that there are large oscillations for the band gaps of single-sided SiH x as a function of H concentration, which is significantly different from that of double-sided SiH x .
Single-sided Si 28 H 6 and Si 24 H 6 have direct (or quasidirect) band gaps of 1.01 and 1.30 eV, respectively, and doublesided Si 16 H 4 and Si 12 H 4 structures have direct (or quasidirect) band gaps of 1.52 and 1.46 eV, respectively.Clearly, these four SiH x compounds have suitable band gaps for solar-absorbing applications.
Interestingly, we also found that double-sided Si 8 H 4 , Si 12 H 8 , Si 16 H 12 , and Si 12 H 10 have the direct (quasidirect) band gaps of 1.85, 1.99, 2.43, and 2.85 eV, respectively, which lie within red, orange, green, and blue colors, as shown in Fig. 5(b).Because Si 8 H 4 , Si 16 H 12 , and Si 12 H 10 can realize the red, green, and blue colors, in a LED application, it may be possible to mix them in order to realize white color.Today, III-nitride materials, e.g., InGaN alloys, have became the frontrunner for achieving phosphors-free white LEDs via the combination of RGB emitters because the alloys with different compositions can, in principle, produce blue, green, and red LEDs [60,61].However, it is known that it is exceedingly difficult to obtain red InGaN LEDs, and the efficiency of green LEDs using InGaN is also relatively low.This is partially because there is a large lattice mismatch (> 10%) between GaN and InN, which can induce significant phase separations and dislocations during the formation of InGaN alloys [60,61].Obviously, the well-ordered SiH x layered structures we discovered here could overcome the large lattice-mismatch issue in InGaN alloys for high-efficiency white lighting.Moreover, it is found that layered materials have unique advantages over the conventional bulk materials for lighting because of the very strong optical transition rates at their band edges [59,62].As far as we know, this is the first report on the discovery of silicon-based materials for white lighting, which can extend our current knowledge of the use of silicon for optoelectronics.We first attempt to understand the electronic and optical properties of Si 28 H 6 , Si 24 H 6 , Si 16 H 4 , and Si 12 H 4 for solar applications.Figure 6 shows the calculated band structures of single-sided Si 28 H 6 and Si 24 H 6 .Si 28 H 6 is a direct-gap semiconductor; i.e., both VBM and CBM are located at the Γ point.The wave function of VBM is contributed mostly by the hybridized π and σ orbitals of three-folded Si atoms at the bottom layer, while the wave function of CBM is contributed mostly by the π orbitals of these special threefolded Si atoms (surrounded by four-folded Si atoms) at the bottom layer, as shown in Fig. 6(a).The partially localized charge distribution gives rise to a relatively flat top valence band and bottom conduction band of Si 28 H 6 .Si 24 H 6 is a quasidirect band-gap material; its global VBM is at the A point, while its global CBM is at the Y point.However, the local VBM at the Y point is only 0.05 eV higher in energy than the global VBM.The plotted wave-function distribution in Fig. 6 Figure 7 shows the calculated band structures of doublesided Si 16 H 4 and Si 12 H 4 .Si 16 H 4 is a direct band-gap semiconductor.Its VBM is contributed by the σ orbitals of all the Si atoms.Interestingly, we find that the wave function of CBM is contributed not only by the 3s electrons of these Si atoms with adsorbed H atoms, but also by the nearly free-electron (NFE) states, which are localized inside of the benzene-ring-like Si atoms (without adsorbed H atoms), as shown in Fig. 7(a).Our further calculations show that the electron effective mass at CBM is around 1.04 m e (in units of free-electron mass), which is an important feature of NFE states.Because the NFE states are not localized on the lattice site of a material, in principle, it will be less affected by structural defects and, therefore, could realize stable charge transport.It has been reported that NFE states can exist in isolated crystalline carbon sheets and nanotubes [63][64][65][66], and this is the first report that NFE states can also exist in silicon materials.The Si 12 H 4 is a quasidirect semiconductor.The global VBM of this structure is at the Γ point, while the global CBM is at the X point.However, the local CBM at the Γ point is only 0.07 eV higher than the global CBM.The wave function of VBM of Si 12 H 4 is contributed mostly by the σ orbitals of all the Si atoms, while the wave function of CBM at the Γ point is contributed by the 3s orbitals of these zigzag-chain Si atoms without H atoms, as shown in Fig. 7(b).One unique advantage of Si 12 H 4 for solar applications is that the carrier effective masses are quite small; e.g., the electron and hole effective mass at the Γ point are about 0.16 and 0.09 m e , respectively.A small effective mass usually means high carrier mobility, which combines with partial electron-hole separation [Fig.7(b)], suggesting that Si 12 H 4 could be a good candidate for highefficiency solar cells.
The above results show that Si 28 H 6 , Si 24 H 6 , Si 16 H 4 , and Si 12 H 4 have suitable band gaps in the range of 1.0-1.5 eV, which are good for solar-cell applications.To further investigate their suitability, we have calculated the absorption spectra for these four structures, compared to the reference air-mass 1.5-solar-spectral irradiance [67], as shown in Fig. 8.The absorbance AðωÞ of monolayer HBS is defined as the fraction of photons with energy E ¼ ℏω absorbed by the HBS [68,69].It can be calculated as where ε 2 is the imaginary part of the dielectric [62,70], c is the speed of light, and Δz is the size of the supercell in the layer-normal direction.Equation ( 5) is the approximation of the absorbance AðωÞ ¼ 1 − e −α•Δz  (α ¼ ε 2 ω=cn) for a monolayer material with small thickness Δz.The monolayer absorbance AðωÞ is independent of the size of the vacuum layer because ε 2 ∝ 1=Δz when a vacuum is included to simulate HBS.Then, we can define the flux of absorbed photons J abs [69] as where E g is the optical gap of the absorber and J ph ðEÞ is the incident photon flux [67,69].J abs can be expressed as the equivalent short-circuit electrical current density in the ideal case when all the photons are converted to carriers and extracted during the PV process.Our calculations show that the J abs for Si 28 H 6 , Si 24 H 6 , Si 16 H 4 , and Si 12 H 4 structures are 8.6, 7.4, 6.9, and 6.5 mA= cm 2 , respectively.Considering that the J abs of 1-nm-diamond Si is only 0.1 mA=cm 2 [69], this means that 60-90-nm-thick Si is necessary to absorb the same fraction of sunlight as these subnanometer-thick HBS.Clearly, the use of HBS-based thin-film solar cells can largely reduce the cost of silicon PV modules, which may have the potential to overcome the big drawback of diamond-silicon-based solar cells.The significantly high optical absorbance of HBS structures compared to silicon is mainly due to the narrowed band gaps and dipole-allowed transitions at the band edges.To maximize the solar-cell efficiency, thicker multilayer stacking of these HBS structures in a bulk heterojunction manner may be needed in practice.
Finally, we study the band structures of double-sided Si 8 H 4 , Si 16 12 , and Si 12 H 10 , which are proposed to be candidates for realizing RGB colors for white lighting.As shown in Fig. 9(a), Si 8 H 4 is a direct band-gap material and its CBM and VBM are both located at the Γ point.The VBM wave function of this structure is contributed by the Si σ orbitals, while the wave function of CBM [Fig.9(b)] is contributed by the 3s orbitals of these Si atoms underneath the surface.Similar to Si 8 H 4 , the wave function of VBM for the structure of Si 16 H 12 is contributed by Si σ orbitals, and CBM is contributed by Si 3s orbitals.Si 12 H 10 is a quasidirect band-gap semiconductor, as shown in Fig. 9(c); its VBM is located at the Γ point, while the global CBM is located at the M point.However, the bottom conduction band at the Γ point is only 0.08 eV higher in energy than that of global CBM.As shown in Fig. 9(c), the wave-function characters at CBM and VBM are similar to those of Si 8 H 4 and Si 16 H 12 .Clearly, these three SiH x ground states are suitable for lighting emitters to achieve RGB colors.In practice, multilayer stacking of HBS structures may be used to obtain bright emission.
In conclusion, we have found that hydrogenation of bilayer silicene can induce some well-ordered intermediate ground states with excellent optoelectronic properties, as summarized in Figure 10.At low hydrogen concentrations, four SiH x ground states, i.e., Si 28 H 6 , Si 24 H 6 , Si 16 H 4 , and FIG. 1.(a) The structure and symmetry of five BS structures with AA or AB stacking.The formation energy E f of each structure with respect to single-layer silicene is also plotted.(b) The phonon spectrum of the AA-3 structure.(c) The fluctuation of total energy of (100-atoms/cell) the AA-3 structure as a function of the molecular-dynamic simulation step at 600 K.(d) The calculated band structure of the AA-3 structure.

FIG. 2 .
FIG. 2. (a) The calculated formation energies E f of single-sided SiH x along with the corresponding CE fits as a function of x.The E f of all the symmetry-inequivalent structures calculated from CE are also plotted here.Inset: The top and side views of the structures of SiH 0.5 .Panel (b) is the same as (a) but for double-sided SiH x .The top and side views of the SiH 1 structure are also shown in Fig. 2(b).

FIG. 5 .FIG. 6 .
FIG. 5.The calculated band gaps of (a) single-sided SiH x and (b) double-sided SiH x ground states as a function of hydrogen concentration.In panel (b), a sketch of light spectrum is overlaid to aid visualization of the size of band gap.

FIG. 7 .
FIG. 7. The calculated band structures of double-sided (a) Si 16 H 4 and (b) Si 12 H 4 .The wave functions of VBM (bottom figure) and CBM (top figure) at the Γ point for each structure are also plotted here.The Fermi level is set to zero.

FIG. 9 .
FIG. 9.The calculated band structures of double-sided (a) Si 8 H 4 , (b) Si 16 H 12 , and (c) Si 12 H 10 .The wave functions of VBM (bottom figure) and CBM (top figure) at the Γ point for each structure are also plotted here.The color for each band gap is also shown.The Fermi level is set to zero.
for Si 16 H 2 (C 2v symmetry), Si 28 H 6 (C 1 symmetry), Si 24 H 6 (C 2 symmetry), Si 28 H 8 (C 2 symmetry), Si 12 H 4 (C 2v symmetry), and Si 16 H 6 (C 2v symmetry).One common characteristic of these ground states is that the adsorbed H atoms on the top of some specific Si atoms break the underneath Si-Si bonds and induce some local structural distortions.The average Si-Si bond length The Fermi level is set to zero.