Cite this Article
Zhao Zong-Yan, Yang Wen, Yang Pei-Zhi. Electronic structure of O-doped SiGe calculated by DFT + U method. Chinese Physics B, 2016, 25(12): 127101  
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Electronic structure of O-doped SiGe calculated by DFT + U method
Zhao Zong-Yan1, 2, †, , Yang Wen3, Yang Pei-Zhi3
Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China
Yunnan Key Laboratory of Micro/Nano Materials & Technology, School of Materials Science and Engineering, Yunnan University, Kunming 650504, China
Key Laboratory of Advanced Technique & Preparation for Renewable Energy Materials (Ministry of Education), Yunnan Normal University, Kunming 650092, China

 

† Corresponding author. E-mail: zzy@kmust.edu.cn

Project supported by the Natural Science Foundation of Yunnan Province, China (Grant No. 2015FB123), the 18th Yunnan Province Young Academic and Technical Leaders Reserve Talent Project, China (Grant No. 2015HB015), and the National Natural Science Foundation of China (Grant No. U1037604).

Abstract
Abstract

To more in depth understand the doping effects of oxygen on SiGe alloys, both the micro-structure and properties of O-doped SiGe (including: bulk, (001) surface, and (110) surface) are calculated by DFT + U method in the present work. The calculated results are as follows. (i) The (110) surface is the main exposing surface of SiGe, in which O impurity prefers to occupy the surface vacancy sites. (ii) For O interstitial doping on SiGe (110) surface, the existences of energy states caused by O doping in the band gap not only enhance the infrared light absorption, but also improve the behaviors of photo-generated carriers. (iii) The finding about decreased surface work function of O-doped SiGe (110) surface can confirm previous experimental observations. (iv) In all cases, O doing mainly induces the electronic structures near the band gap to vary, but is not directly involved in these variations. Therefore, these findings in the present work not only can provide further explanation and analysis for the corresponding underlying mechanism for some of the experimental findings reported in the literature, but also conduce to the development of μc-SiGe-based solar cells in the future.

PACS: 71.20.–b;71.20.Nr;81.05.Hd;82.20.Wt
Keyword:SiGe alloys;O doping;electronic structure;density functional theory (DFT) calculations
1. Introduction

As the world’s population is continuously increasing exponentially, the need for energy is forecasted to double the today’s requirement for energy by the end of 2025. At present, world energy demand is mostly satisfied by the fossil fuels, which have limited available resources (for example: oil exploitation limit is 43 years; coal exploitation limit is 231 years; natural gas exploitation limit is 62 years; nuclear exploitation limit is 73 years).[1–3] Furthermore, another important consideration of increasing fossil fuel consumption is the influence on environment,[4] for example, burning coal will emit 322.8 g/kW·h of CO2, 1.8 g/kW·h of NOx, and 3.4 g/kW·h of SOx. Therefore, the urgent challenge is to develop and exploit renewable, environment-friendly energy sources. Out of different renewable energy sources known today, solar energy is one of the most abundant, clean, and effective energy sources. The photovoltaic (PV) technology is the most important solar energy application, which can directly harvest and convert solar energy into usable and storable electric energy. However, there are two most drawbacks of PV technology, which hinder its industrial application, i.e., the low conversion efficiency and high production cost.

In the case of device design for solar cells, light management is one of the most important topics. Because most Si-based materials belong to indirect band gap semiconductors, so thin film whose thickness is less than 2 μm could not guarantee to absorb enough solar light. Thus, improving the efficiency of Si-based solar cells must improve the solar light absorption. For this purpose, some light trapping structures (for example, p–i–n or n–i–p device structures, textured substrates, etc.) have been designed to enhance light absorption and improve energy conversion efficiencies.[5] On the other hand, Si–Ge alloying could also achieve this purpose. Matsui et al. fabricated microcrystalline (μc) Si1−xGex thin film by plasma-enhanced chemical vapor deposition, which exhibits infrared response even higher than that of double-thickness microcrystalline Si thin film, and found the optical absorption increases with the increase of Ge content. They have achieved a 6.3% efficiency of a single junction p–i–n solar cells by using a 1-μm-thick μc-Si0.8Ge0.2:H i-layer, which shows excellent performance stability under prolonged light soaking.[6,7] Due to the optical band gap of SiGe alloy decreases with the increase of Ge content and, therefore its optical band gap could be continuous adjusted in a wide range from ∼ 1.1 eV to ∼ 0.66 eV via changing the component proportion in the film. It has the ability to expand absorption of solar spectrum and improve the conversion efficiency of solar cells. This advantage of continuously adjustable band gap makes SiGe alloy thin film used as the intermediate or bottom absorber layer in the multi-junction tandem solar cells.[8] In addition, because its absorption coefficient is 1–2 orders of magnitude higher than that of silicon material, so it could be prepared into thinner film. The latter could shorten the process time and reduce the cost of raw material, which are also important for the industrial production. These advantages make it arouse a great deal of research interesting solar cells applications. Matsui et al. replaced the conventional μc-Si:H with the μc-Si1−xGex:H as infrared absorber in double junction tandem solar cells, in which the bottom cell thickness can reduce more than half while preserving the current matching with hydrogenated amorphous silicon (a-Si:H) top cell. Finally, they obtained an initial efficiency of 11.2% for a-Si:H/μc-Si0.9Ge0.1:H solar cell with bottom cell thickness less than 1 μm.[9]

However, if Ge is incorporated into Si material, the properties of structure and electrics are also consequently changed. Importantly, the bond energies of Ge–Ge bond and Ge–H bond are weaker than those of Si–Si bond and Si–H bond, leading to H atoms’ prior bonding with Si atoms. As a result, the passivation of Ge dangling bond is deficiency, and there are more Ge dangling bonds in SiGe thin film. And when the Ge content is larger than 0.3, the photovoltaic performance begins to degrade: the conduction band tail width is broadened, the electron transfer rate decreases, and the carrier transport is worsened.[10–12] Matsui et al. also found the solar cell parameters for larger Ge contents are lowered by increasing the charge carrier recombination in the μc-Si1−xGex:H layer, and the photocarrier transport in the solar cells for x > 0.2 is dominated by the carrier recombination due to the increased dangling bond defects and the illumination-induced field distortion in the i-layer.[6,7] Recently, Bidiville et al. found that the short-circuit current density of μc-SiGe p–i–n solar cells increases almost 4 mA/cm2 due to oxygen doping. And, they attributed this effect to the oxygen doping compensating for the space charges caused by the germanium dangling bounds rather than the direct defect passivation.[13] In their experiment, the oxygen doping of the i-layer was conducted by using 1% CO2 diluted in H2, because the required gas flow is so small that a diluted gas must be used. During crysctalization of μc-SiGe, oxygen impurities adsorb onto the surfaces or grain boundaries (i.e., surface doping, including the occupation of surface vacancy or replacement of surface atom), and then diffuse into bulk (i.e., bulk doping, including occupation of inner vacancy or replacement of host atom).

In fact, the conversion efficiency of ∼ 1.2-μm-thick μc-Si:H solar cells is deteriorated if the oxygen content in absorber layers exceeds the range from 1.2 × 1019 cm−3 to 2 × 1019 cm−3. Efficiency losses due to the fact that the oxygen impurities lead to the decreases of both fill factor and external quantum efficiency at wavelengths of >500 nm.[14,15] However, a few published articles are available to compare the doping effects of oxygen between μc-Si and μc-SiGe. Motivated by the experimental work in Ref. [13], we believe that it is necessary to systematically study the relationship between electronic structure and photovoltaic performance of O-doped μc-SiGe, in order to develop efficient μc-SiGe-based solar cells. Thus, in the present work, the crystal structure and electronic structure of O-doped SiGe are investigated by using density functional theory (DFT) calculations. Moreover, the relationship between electronic structure and photovoltaic properties will be discussed and compared. Based on the calculated results, possible explanations and underlying mechanism for previous experimental observations will be provided.

2. Computational methods and models

In the present work, all of the calculations are carried out by using the periodic density functional theory (DFT) package of Cambridge Serial Total Energy Package (CASTEP) codes.[16] The core electrons (O:[He], Si:[Ne], Ge:[Ar]) are treated as the ultrasoft pseudopotential. The exchange–correlation effects of valence electrons (O:2s22p4, Si:3s23p2, Ge:4s24p2) are described by the revised Perdew–Burke–Ernzerhof for solid (PBEsol) within generalized gradient approximation (GGA).[17] In order to obtain accurate electronic structure, the method of GGA + U is adopted to overcome the well-known shortcoming of GGA,[18] which underestimate the band gap value of semiconductor, via adjusting the parameters of electronic configuration In the present work, the U value of Si\Ge\O-p orbital is set to be Ueff = U − J = 7.90 eV, which have been proved to be efficient for Si-based materials in our previous work.[19,20] Using this GGA+U method, we obtain the accurate band gaps of c-Si (1.119 eV), c-Ge (0.743 eV), α-SiO2 (8.718 eV), which are much close to the experimental measurements. In the DFT calculations, the quality setting affects all relevant task parameters that control the precision of the simulation, which includes the basis set, k-point, and SCF convergence criteria, along with the convergence criteria for the geometry optimization. In order to ensure the accuracy of the results, as well as the convenience of direct comparison, we set it up to the highest standard (i.e., ultra-fine) in the present work. The Monkhorst–Pack scheme k-points grid sampling is set to be 4 × 4 × 2 for the irreducible Brillouin zone. A 60 × 60 × 80 mesh is used for fast Fourier transformation. An energy cutoff of 380 eV is used for expanding the Kohn–Sham wave functions. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) scheme is chosen as the minimization algorithm.[21] Its convergence criteria are set as follows: the force on the atoms is less than 0.03 eV/Å, the stress on the atoms is less than 0.05 GPa, the atomic displacement is less than 1 × 103 Å, and the energy change per atom is less than 1 × 105 eV. Based on the optimized crystal structure, the electronic structure and the optical properties are then calculated. The band structures are calculated along the paths connecting the high-symmetry points.

For the Si1−xGex alloy, there are lots of possible structural configurations, most of which are disorder alloys. In order to clearly understand the doping effect of oxygen, we use cubic Si0.5Ge0.5 alloy configuration (in the context, it is abbreviated by SiGe) with the symmetry of and the lattice constant of 5.5955 Å as the original model as shown in Fig. 1.

Fig. 1. Crystal structure of SiGe.

In this original model, the Ge content is equal to Si content, and Ge atom occupies the equivalent lattice site of Si atom. Choosing this composition we can directly compare the effects of doping oxygen on different positions. In the cases of bulk doping, a 2 × 2 × 2 supercells are used for constructing the O-doped SiGe models. In other words, the original supercells are 11.191 × 11.191 × 11.191 Å3, which is large enough to avoid the self-interaction between impurities in the periodic boundary conditions. To set the substitutional doping model, which is denoted as SiGe:O@Si or SiGe:O@Ge in the following context, one Si or Ge atom in the supercell is replaced by an O atom; while, to set the interstitial doping model, which is represented by SiGe:O@Vac in the following context, an O atom is inserted into the lattice vacancy. In these supercells, the total number of atoms reaches to 64 or 65. In the cases of surface doping, a 3 × 3 super-slab (11.7464 × 11.7464 Å2) for (001) surface or a 2 × 3 super-slab (11.0746 × 11.7464 Å2) for (110) surface (These two surfaces are separated by a 20-Å-thickness vacuum layer) is used for constructing the O-doped SiGe models. Each surface model contains 8 (for (001) surfaces) or 12 (for (110) surfaces) SiGe atomic layers, and thus the size of model along the surface normal direction is larger than 40 Å, which could produce reasonable surficial structure and properties for SiGe. Moreover, in order to mimic the influence of bulk phase, the below half-layers are fixed. To set the substitutional doping model, one Si or Ge atom on the topmost layer is replaced by an O atom; while, to set the interstitial doping model, an O atom is placed onto the surface vacancy. In these surpercells, the total number of atoms reaches to 144 or 145. For the case of interstitial doping model, we first consider all kinds of lattice vacancies, and then compare the total energies, and finally choose the model with the minimum total energy as the stable model in the present work.

3. Results and discussion
3.1. Bulk doping

Owing to the ionic bonding existing between O impurity and Si or Ge atom, the bond lengths of Ge–O (2.1531 Å) and Si–O bond (2.2310 Å) in the substitutional doping models (SiGe:O@Si, and SiGe:O@Ge) are shorter than the bond length of Si–Ge bond (2.4229 Å), and their crystal volumes are slightly contracted. At the same time, the symmetry of substitutional doping models is changed into . In the case of interstitial doping model (SiGe:O@Vac), the most stable configuration is that O impurity is located in the center of Si–Ge hexatomic ring, with bond lengths of 1.9092 Å for Si–O bonds and 2.7261 Å for Ge–O bonds respectively. The corresponding crystal volume is slightly expanded, and the symmetry is changed into R3m. In the DFT study, the conception of impurity formation energy (Ef) is usually used to determine the difficulty degree for impurity to be incorporated into host crystal lattice, which is a widely accepted approach. In the present work, the formula of impurity formation energy is referred to the formalism defined by Van de Walle and Neugebauer.[22] The impurity formation energy of O-doped SiGe is also listed in Table 1. For bulk doping, the impurity formation energy of O impurity to replace Si or Ge is negative, while that of O impurity to occupy the lattice vacancy is positive. These calculated results imply that the process for O impurity to be incorporated into host to replace host atoms is easier than to occupy the lattice vacancy. What is more, these Ef values are relatively small. Thus, the preparation O-doped SiGe sample is relatively unproblematic in experiments.

Table 1.

Impurity formation energies of O-doped SiGe with different doping configurations.

.

The calculated band structures of pure SiGe and different O-doped SiGe’s are shown in Fig. 2. In the case of pure SiGe, both valence band maximum (VBM) and conduction band minimum (CBM) are located at different k-points, indicating that pure SiGe is also an indirect band gap semiconductor with a band gap of 1.018 eV. While in the O-doped SiGe model, the type of band gap is the direct band gap (for SiGe:O@Vac) or close to the direct band gap (for SiGe:O@Si or SiGe:O@Ge). And the band gaps are obvious narrowed, which are further advantageous for infrared light absorption. At the same time, the spin-up states and the spin-down states are completely coincident for pure SiGe and all bulk doping models (so the spin–orbit coupling effect is not shown in the following figure for the density of sates). Furthermore, the features of band structures of SiGe:O@Si and SiGe:O@Ge are very similar, except the values of band gaps. And there are small unoccupied states above the Fermi energy level (EF), in other words, the EF crosses the top part of valence band of SiGe:O@Vac. Besides the above doping effects, the energy states that are induced by O doping are observed in none of band gaps for all bulk doping models.

Fig. 2. Band structures of O-doped bulk SiGe, calculated by different ways. The blue lines represent spin-up states; the red curves refer to spin-down states, in which the spin-up states and spin-down states are completely overlapping.

Combined with above mentioned band structures, the total and partial density of states (DOS) of pure SiGe and O-doped SiGe are plotted in Fig. 3, in order to analyze the chemical bonding information. For pure SiGe, the top of VB is mainly composed of Si-3p and Ge-4p states, in which Si-3p states have the equal contribution to Ge-4p states; the bottom of CB is mainly composed of Ge-4s states. For the O doping models, the first variation is that the DOS peaks, which are located at the top of VB and the bottom of CB, are obviously stronger. Combined with the corresponding energy levels near the band gaps in Fig. 2. These energy states induced by O doping could provide more photo-generated carriers than in pure SiGe. In the case of SiGe:O@Si, the contribution of Ge-4p states to the top of VB is predominant, while in the case of SiGe:O@Ge, the contribution of Si-3p states to the top of VB is predominant. In the case of SiGe:O@Vac, the composition of the top of VB is similar to that in the case of pure SiGe, in which Ge-4p states have slightly larger contribution. And in all these models, the bottom of CB is dominantly composed of the Ge-4s states. Moreover, the contribution of O-2s states to electronic structure is located in an energy range of −19∼–17 eV, while the contribution of O-2p states is located in an energy range of −10∼–2.5 eV for the middle and bottom of VB. These calculated results suggest that O doing mainly induces the electronic structures near the band gap to vary, but is not directly involved in these variations.

Fig. 3. Total and partial densities of states of O-doped bulk SiGe, calculated by different ways.
3.2. (001) surface doping

For the SiGe (001) surface, there are two possible terminated planes: the utmost-top plane is for all Si atoms or Ge atoms. That is to say, all the dangling bonds on the terminated plane are either Si dangling bonds or Ge dangling bonds, and they are denoted by SiGe (001)–Si surface or SiGi (001)–Ge surface in the following context. In the present work, the calculated surface energies of these two surfaces are respectively 1.620 J/m2 for SiGe (001)–Si surface and 1.724 J/m2 for SiGe (001)–Ge surface, so the Si atoms could be mainly exposed on the SiGe (001) surface. The most stable surface doping configurations that are obtained by geometry optimization are illustrated in Figs. 4 and 5.

Fig. 4. Top panels: the stable configurations of O-doped SiGe (001)–Si surface (Only the top SiGe bi-layer is shown here.); Middle panels: the corresponding contour maps of electron density; bottom panels: the corresponding contour maps of electron density difference.
Fig. 5. Top panels: the stable configurations of O-doped SiGe (001)-Ge surface (Only the top SiGe bi-layer is shown here.); middle panels: the corresponding contour maps of electron density; bottom panels: the corresponding contour maps of electron density difference.

For the pure surface, the surface relaxation is very significant: the outmost top atoms are upward shifting by ∼ 0.2 Å. In the case of SiGe (001)–Ge surface, the surface reconstruction is negligible; while in the case of SiGe (001)–Si surface, the surface reconstruction is very significant: Si atoms on the outmost top layer are shifted by ∼ 1 Å along the direction. After doping O atoms, the Si1 atoms (Fig. 4) and Ge1 atoms (Fig. 5) in the first SiGe bi-layer are obviously shifted from the balance positions compared with along the pure (001) surface, while the displacements of the atoms in the second SiGe bi-layer (Si2 and Ge2 in Figs. 3 and 5 respectively) are very small. In the case of SiGe (001)–Si surface: O@Si, the bond length of Ge–O bond is 1.8534 Å, while the bond lengths of neighboring Si–Ge bonds are obviously expanded, due to the stronger repulsive interactions induced by O doping. Thus, the EF value of SiGe (001)–Si surface: O@Si is very high (another reason is that the lattice constants parallel to the surface are constrained in the geometry optimization). In the case of SiGe (001)–Si surface: O@Vac, the most stable position of O impurity is the on-top site above the Si1 atom with a bond length of 1.5391 Å (Si1–O bond). And the neighboring Si1 atoms are also repelled away, and some of Si1 atoms form Si–Si bonds each with a bond length of ∼ 2.36 Å. The corresponding EF value of SiGe (001)–Si surface: O@Vac is very lower than that of SiGe (001)–Si: O@Si. In the case of SiGe (001)–Ge surface: O@Ge, the bond length of Si–O bonds is 1.6905 Å. And the neighboring Si1 atoms are also repelled away, and some of Ge1 atoms form Ge–Ge bonds each with a bond length of ∼ 2.56 Å. In the case of SiGe (001)–Ge surface: O@Vac, the most stable position of O impurity is the on-top site above the Ge2 atom and the O atom bonds with neighboring two Si1 atoms (1.7021 Å of Si1–O bonds). And the neighboring Si1 atoms are also repelled away, and some of Si1 atoms form Si–Si bonds each with a bond length of ∼ 2.36 Å, while other Si1 and Ge1 atoms are also slightly attracted together. The EF value of SiGe (001)–Ge: O@Vac is obviously smaller than that of SiGe (001)–Ge Surface: O@Ge.

In Figs. 4 and 5, the contour maps of electron density and electron density difference on the top plane of these surfaces are plotted. For SiGe (001) surface, there is a stronger covalent bond between Si and Ge atoms, and more electrons are gathering onto Si1 atoms. On the SiGe (001)–Si surface: O@Si, the electrons transfer from Si1 to O impurity or Si1–Ge1 covalent bonds, so the electron density of Si1 decreases. On the contrary, there are no more electrons gathering onto O impurity, and the electron density of Si1 increases on the SiGe (001)–Si surface: O@Vac. In the case of SiGe (001)–Ge surface, the situation is just opposite to that of SiGe (001)–Si surface: more electrons gather on O impurity on O@Ge surface and O@Vac surface; the electron density of Ge1 increases on the O@Ge surface, while the electron density of Ge1 obviously decreases on the O@Vac surface. The variations of electron density and electron density difference of surface by O doping could induce the surface potential and surface charge space to change. In order to quantitatively describe the above variations, the surface work functions of different surfaces are calculated and listed in Table 2.

Table 2.

Surface work functions of O-doped SiGe with different doping configurations and pure surfaces.

.

The surface band structures and the corresponding densities of sates of different O-doped SiGe (001) are illustrated in Figs. 6–9. Compared with bulk SiGe, the pure SiGe (001) surface has broadened band gaps: the band gap of SiGe (001)–Si surface is 1.104 eV, while that of SiGe (001)–Ge surface is 1.216 eV, which is obviously broadened. Furthermore, the types of band gaps of these surfaces are direct band gap or close-to direct band gap. At the same time, the spin-up states and the spin-down states are still completely coincident for pure SiGe surfaces, while the spin-up states and the spin-down states are separated, especially near the Fermi energy level for all surface doping models. In the O-doped SiGe (001)–Si surface, the band gaps are further narrowed. Although the band gaps of O-doped SiGe (001)–Ge surfaces are narrowed, they are still larger than the band gap of bulk SiGi. Furthermore, there are small unoccupied states above the Fermi energy level in the case of pure SiGe (001)–Si surface; in other words, the EF crosses the top part of valence band. Some energy states that are induced by O doping can be observed in the band gaps for surface doping (these energy states are considered as impurity energy states), which is different from the scenario for the bulk doping. In the case of SiGe (001)–Si surface: O@Si, there are an isolated spin-up impurity energy state and an isolated spin-down impurity energy state above VB; while in the case of SiGe (001)–Si surface: O@Vac, there are two isolated spin-up impurity energy states above VB. In the case of SiGe (001)–Ge surface: O@Ge, there is no impurity energy state in the band gap; while in the case of SiGe (001)–Ge surface: O@Vac, there are two impurity energy states almost coincided between spin-up and spin-down impurity energy states above VB.

Fig. 6. Band structures of O-doped SiGe (001)–Si surface, obtained by different ways. The blue curves represent spin-up states; the red curves refer to spin-down states.
Fig. 7. Band structures of O-doped SiGe (001)–Ge surface, calculated by different ways. The blue curves represent spin-up states; the red curves refer to spin-down states.
Fig. 8. Total and partial densities of states of O-doped SiGe (001)-Si surface, calculated by different ways (Only the data of the top SiGe bi-layer are shown here).
Fig. 9. Total and partial densities of states of O-doped SiGe (001)–Ge surface, calculated by different ways (Only the data of the top SiGe bi-layer are shown here.)

The above mentioned features can be further explored in the information provided by DOS. For pure SiGe (001) surface, the surface states are mainly caused by the dangling bonds: the Si-3p states dominantly form the top of VB and the bottom of CB for the SiGe (001)–Si surface; while the Ge-4p states dominantly form the top of VB and the bottom of CB for the SiGe (001)–Ge surface. Moreover, in the case of O-doped SiGe (001)–Si surface, the Si-3p states also dominantly form the impurity energy states above the VB. The O doping causes the DOS peaks on the top of VB and the bottom of CB to become stronger than the scenario in the pure SiGe (001) surface. These calculated results suggest that the surface impurity energy states caused by O doping not only enhance the infrared light absorption, but also improve the behaviors of photo-generated carriers (including: generation, transfer, and so on).

3.3. (110) surface doping

In the present work, the calculated surface energy of SiGe (110) surface is 1.290 J/m2, which is quite obviously lower than the surface energy of SiGe (001) surface. Thus, the (110) surface is easily exposed for SiGe material, especially in μc-SiGe. After surface relaxation, the Ge atoms on the topmost layer are outward shifted by ∼ 0.511 Å, while the Si atoms on the topmost layer are inward shifted by ∼ 0.314 Å. Furthermore, on the second atomic layer, the Ge/Si atoms are outward shifted by ∼ 0.149 Å/∼ 0.233 Å. On the other hand, on the unrelaxed (110) surface, Ge atoms and Si atoms are on the identical plane. This means that the surface relaxation is significant on SiGe (110) surface. Along the surface later directions, Ge atoms on the topmost layer are not obviously shifted, while Si atoms on the topmost layer are shifted by ∼ 0.412 Å along the direction. Thus the surface reconstruction of SiGe (110) surface is caused by the atomic interaction between Si atoms on the topmost layer. In the case of SiGe (110) surface: O@Si, the bond lengths are 2.0595 Å for the higher two Ge–O bonds, and 1.9128 Å for the lower one Ge–O bond, respectively; while in the case of SiGe (110) surface: O@Ge, the bond lengths are 1.8678 Å for the higher two Si–O bonds, and 1.7463 Å for the lower one Ge–O bond, respectively. In the case of SiGe (110) surface: O@Vac, the most stable configuration is the O impurity inserted between a four-coordinated Si2 atom and a three-coordinated Ge1 atom, forming a bridge to link these two atoms, with a bond lengths being 1.6530 Å for Si–O bond and 1.8607 Å for Ge–O bond, respectively. Unlike that on the SiGe (001) surface, the lattice distortion induced by O doping is less prominent on the SiGe (110) surface as shown in Fig. 10. Thus, the EF value of O doping on the SiGe (110) surface is correspondingly lower than that of on the SiGe (001) surface. Especially, the EF value of the SiGe (110) surface: O@Vac is negative. These calculated results imply that the process of the O impurity occupying the vacancy on surface is easier to take place than that of replacing host atoms on this surface, which is different from the situation of bulk doping.

Fig. 10. Top panels: the stable configurations of O-doped SiGe (110) surface (Only the top SiGe bi-layer are shown here.); middle panels: the corresponding contour maps of electron density; bottom panels: the corresponding contour maps of electron density difference.

As shown in the above Fig. 11, for the SiGe (110) surface, there exists a stronger covalent bond between Si atom and Ge atom, in which more electrons gather on the Si1–Ge1 bonds. On the SiGe (110) surface: O@Si, the electrons transfer from Ge1 to O impurity or Si1–Ge1 covalent bonds, so the electron density of Ge1 decreases, while the electron density of Si1 slightly increases. On the SiGe (110) surface: O@Ge, the electrons transfer from Si1 to O impurity or Si1–Ge1 covalent bonds, so the electron density of Si1 decreases, while the electron density of Ge1 slightly increases. On the SiGe (110) surface: O@Vac, there are outstanding more electrons gathering onto the O impurity, and the electron densities of Si1 and Ge1 decrease. As a result, the surface work functions of these O-doped SiGe (110) surfaces decrease with the composition on the pure SiGe (110) surface as listed in the previous Table 2.

Fig. 11. Band structures of O-doped SiGe (110) surface, calculated by different ways. The blue curves represent spin-up states; the red curves refer to the spin-down states.

The surface band structures and the corresponding densities of sates of different O-doped SiGe (110) surfaces are illustrated in Figs. 11 and 12. Compared with bulk SiGe, the pure SiGe (110) surface has obviously narrowed band gap (0.234 eV), because there are abundant surface states existing in the band gap. Furthermore, the type of band gap of SiGe (110) surface is an indirect band gap, and the spin-up states and the spin-down states are still completely coincident. In the O-doped SiGe (110) surface, the band gaps are broadened. For SiGe (110) surface: O@Si, there is no impurity energy state in the band gap. While, there some energy states could be observed in the band gap for SiGe (110) surface: O@Ge or O@Vac. What is more, in the case of SiGe (110) surface: O@Vac, the impurity energy states almost fill the whole band gap. Thus, it is difficult to estimate the real surface band gap of SiGe (110) surface: O@Vac (the value denoted in Fig. 11 is roughly estimated by the feature of band structure in comparison with pure SiGe (110) surface). For pure SiGe (110) surface, the surface states are mainly caused by the dangling bonds: the Si-3p states and Ge-4s/4p states dominantly form the top of VB, and the Ge-4p states dominantly form the bottom of CB. Moreover, the Si-3p states and Ge-4s/4p states also dominantly form the impurity energy states in the cases of SiGe (110) surface: O@Ge and O@Vac. Compared with pure SiGe (001) surface, O doping causes DOS peaks on the top of VB and the bottom of CB to become more stronger. These calculated results suggest that the surface impurity energy states caused by O doping not only enhance the infrared light absorption, but also improve the behaviors of photo-generated carriers. In order to further explore the impurity energy states on the surface, figure 13 provides the layer-resolution DOS of SiGe (110) surface: O@Vac. Because O impurity strongly interplays with the unsaturated atoms, the electronic structure of first SiGe layer is obviously different from those of other SiGe layers and bulk SiGe. As the O impurity is away from the surface, its doping effect gradually becomes weaker, and the electronic structures in these SiGe layers present some features of the electronic structure of bulk SiGe. In the process, the impurity energy states in the band gap gradually disappear, and finally could not be observed in the 5th SiGe layer. According to these calculated results, one could consider that the surface doping effect of O impurity is a relatively localized effect that exists in an about 10-Å-thick surface.

Fig. 12. Total and partial densities of states of O-doped SiGe (110) surface, calculated by different ways (Only the data of the top SiGe bi-layer are shown here.)
Fig. 13. Lay-resolutions of density of states of SiGe (110) surface: O@Vac, in comparison with those of bulk SiGe.
4. Summary and conclusion

Firstly, because the surface energy of SiGe (110) surface is obviously lower than those of SiGe (001) surfaces, this surface may predominately be exposed in the μc-SiGe material. Thus, for p–i–n absorber layer, the surface property of SiGe (110) surface is a key factor to the final photovoltaic performance of μc-SiGe-based solar cells. In order to understand the electronic structure of O-doped SiGe, the bulk, (001) surface, and (110) surface are chosen as the research objects, and the relevant micro-structures and properties are calculated by DFT + U method in the present work. The lattice distortions caused by O doping for bulk SiGe are not obvious. In the case of surface doping, O impurity leads to the significant surface relaxation or surface reconstruction on the topmost layers. The impurity formation energy of O interstitial doping is lower than that of O substitutional doping for surface model, implying that O impurity prefers to occupy the lattice vacancy site on SiGe surface. By O doping, the band gaps are slightly narrowed, except in the case of O-doped SiGe (110) surface. Importantly, there are abundant impurity energy states in the band gap of O@Vac surface model. These doping effects not only enhance the infrared light absorption, but also improve the behaviors of photo-generated carriers. On the other hand, the surface charge and potential decrease in the cases of SiGe (001)–Ge surface: O@Vac and SiGe (110) surface O@Vac, in which (001)-Ge surface and (110) surface have the lower surface energies, and the corresponding impurity formation energy of O interstitial doping is lower. Thus, the reducing surface work function could confirm previous experimental observation: oxygen doping can compensate for the space charges caused by the germanium dangling bonds. In all cases, O doing mainly induces the electronic structures near the band gap to vary, but is not directly involved in these variations. The findings in the present work could well explain the experimental observations in the literature, and conduce to the development of μc-SiGe-based solar cells.

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