Self-trapping in B-doped amorphous Si: Intrinsic origin of low acceptor efficiency

Self-trapping in B-doped amorphous Si: Intrinsic origin of low acceptor efficiency I. Santos,1,2,*P. Castrillo,2W. Windl,1D. A. Drabold,3L. Pelaz,2and L. A. Marqués2 1Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, Ohio 43210-1178, USA 2Departamento de Electricidad y Electrónica, Universidad de Valladolid, ETSI de Telecomunicación, 47011 Valladolid, Spain 3Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701-2979, USA 共Received 4 November 2009; revised manuscript received 23 December 2009; published 19 January 2010兲 We have used ab initio simulations to study the doping efficiency of amorphous semiconductors, in particular of B-doped amorphous Si. We have found that even in the optimum case of substitutional doping in dangling-bond free amorphous Si the holes provided by B atoms do not behave as free carriers. Instead, they are trapped into regions with locally distorted bond angles. Thus, the effective activation energy for hole conduction turns to be the hole binding energy to these traps. In the case of high B concentration, the trap states move deeper in the gap and the binding energy and spatial localization of holes increase. In addition, B atoms have lower energies for shorter bond lengths, configurations favored in the vicinity of these traps. DOI: 10.1103/PhysRevB.81.033203 PACS number共s兲: 31.15.A⫺, 71.55.Jv, 81.05.Gc The possibility of doping amorphous Si 共a-Si兲and hydrogenated amorphous Si 共a-Si:H兲and their lower production cost with respect to crystalline Si 共c-Si兲have made them the materials of choice for many different applications in optoelectronics and photovoltaics.1Nevertheless, these materials have an unexpected low doping efficiency,2which limits their use in device applications. Doping in amorphous materials poses various interesting questions not encountered in crystals. In tetrahedral amorphous semiconductors, dopants are thought to become electrically active when they are in a fourfold configuration, known as substitutional doping, and thus they can provide the material with a carrier.3However, relaxation effects in the amorphous matrix can be substantial after the incorporation of dopants so that it is not obvious a priori whether they will end in a doping configuration or not.2In addition, amorphous networks have tail states in the valence and conduction bands 共usually of exponential “Urbach” form兲that may be localized or extended 共albeit with poor connectivity兲in space,4as well as localized midgap states commonly associated to dangling bonds 共which are induced by threefold coordinated Si atoms兲.2Experiments indicate that the majority of the excess carriers introduced by dopants does not occupy shallow tail states as it would be expected in an ideal intrinsic material but rather midgap states.2In addition, it has been also found that the carrier mobility is degraded and the activation energy for conduction increases when increasing the dopant concentration,5findings that are characteristic of highly localized trapping states. As a consequence, the doping efficiency is reduced. Several plausible arguments have been developed for explaining these observations. Some authors proposed that dopants induce midgap states,2,5while others, based on experiments6and subsequent calculations,7argued that H passivation plays an important role in a-Si:H, the material of interest for photovoltaic applications rather than pure a-Si. In both arguments the low doping efficiency is attributed to the influence of external factors, namely, dopants or H atoms. Apart from these widely accepted factors, there are indications that carrier traps can also be generated by highly distorted bonds. Using tight-binding calculations Bagolini et al.8found that distorted bond angles can localize electronic states in a-Si. Using ab initio calculations Wagner et al.9found that optical excitations can generate distorted bond angles in a-Si, which act as hole traps. In addition, other theoretical works found that sufficiently distorted bond angles generate midgap levels rather than shallow levels without the intervention of dangling bonds or floating bonds 共which are induced by fivefold Si atoms兲.10 Nevertheless, the present understanding of how these traps may influence the free-carrier concentration is rather incomplete. In this work we have used ab initio simulations to address the analysis of the low doping efficiency of B-doped a-Si, the main p-type dopant in Si. We focus our study on substitutional B doping of dangling bond free pure a-Si. This can be considered the most ideal situation not influenced by any external factor and the limit case for an optimal technological matrix. In this scenario, we analyze the spatial localization of the holes introduced by B atoms, and the electronic density of states 共EDOS兲of the resulting doped material in order to evaluate the possible role of intrinsic features of the amorphous matrix in controlling the free hole concentration. For this Brief Report we employ two different cubic a-Si cells containing 64 and 216 atoms, which are generated using the procedure proposed by Barkema and Mousseau.11 The calculations presented in this work are referred to the 64-atom cell, while the 216-atom cell is used to test the obtained findings in a larger simulation cell. Periodic boundary conditions are employed in all spatial directions. We use the density-functional theory code VASP 共Refs. 12 and 13兲with generalized gradient approximation ultrasoft pseudopotentials.14 The energy cutoff chosen is 230 eV in all calculations. We use a 4⫻4⫻4 Monkhorst-Pack k-point mesh for EDOS calculations in the 64-atom cell, and 2⫻2 ⫻2 for cell relaxations, and also for EDOS calculations in the 216-atom cell. Although the amorphous simulation cells are generated externally to VASP, they barely change at all when they are relaxed with ab initio interactions. After this relaxation all the Si atoms in the amorphous cells are fourfold coordinated, i.e., there are neither dangling nor floating bonds. While the atomic bond lengths and bond angles in c-Si are dc-Si=2.36 Å and ␪ c-Si=109.47°, the corresponding averaged values in the a-Si cells used are da-Si =2.37⫾0.08 Å, and ␪ a-Si=109⫾10°, respectively. These PHYSICAL REVIEW B 81, 033203 共2010兲 1098-0121/2010/81共3兲/033203共4兲©2010 The American Physical Society033203-1 values are within the expected range of well-relaxed computer-generated a-Si cells.11,15 We have considered 64 different B configurations by successively replacing each of the Si atoms of the 64-atom cell by a B atom. By sampling all 64 sites, we accumulate some reasonable statistics. We performed relaxations of both the atomic positions and cell shape and volume to find the nearest local minimum energy configuration for each replacement. In all the resulting structures, B atoms are fourfold coordinated, and thus, they are expected to provide the sample with one hole. The average B bond length is 2.07⫾0.06 Å, in agreement with the obtained in c-Si of 2.08 Å. In the case of an ideal acceptor, the hole would be in a shallow state locally extended around the dopant.16 However, this did not happen in our simulations. In Fig. 1we represent the hole localization for different B configurations in the 64-atom cell. For the configuration shown in Fig. 1共a兲, the hole is localized far from the B atom. In fact, we found that, independently of the position of the B atom, the hole is localized at the same region of the cell with a similar density distribution. This region is represented in Fig. 1by the colored Si atoms, and the hole localization by the shadowed areas. When the B atom is situated at this region 关Fig. 1共b兲兴, the hole-localization is even stronger. We have also analyzed the situation where two Si atoms are replaced by B, representing the case of high dopant concentration. For that purpose, we selected two Si atomic positions more than 7 Å apart from the red atoms of Fig. 1and ⬃5.5 Å from each other. The resulting configuration is shown in Fig. 1共c兲, together with the spatial localization of the holes provided by B atoms. As it can be seen, the holes are again at the same zone, and not in the neighborhood of B atoms. To elucidate whether the hole-localization region is induced by the B atoms or it exists even in the absence of acceptors, we analyzed the undoped 64-atom cell with positive charge, 共a-Si64兲+, i.e., with the same number of electrons than the studied neutral B configurations, 共a-Si63B兲0. The resulting hole localization, shown in Fig. 1共d兲, is very similar to that of Fig. 1共a兲. We also considered the case of adding two holes to the a-Si cell 共not shown兲and their localization agreed with that shown in Fig. 1共c兲. Therefore, the region of interest is not induced by the B atoms but it is inherent to the a-Si matrix. In this sample we have found that when there are not holes available in the cell 关for example, in 共a-Si64兲0 or 共a-Si63B兲−configurations not shown in Fig. 1兴, some of the bond angles at the hole-localization region are ⱗ90°. When one hole is captured 关Figs. 1共a兲,1共b兲, and 1共d兲兴, the bond angles in the colored zigzag become more distorted 共⬍85°兲, and the distortion is even higher when two holes are captured, with angles ⬃75° 关for example, in Fig. 1共c兲兴. Furthermore, one of the Si atoms involved in the holelocalization region 关in particular the Si atom replaced by B in Fig. 1共b兲兴is almost in a “flat configuration” in all the charge states, i.e., with three angles adding ⬃360°. The relation between distorted bond angles and hole localization agrees with previous studies.8,9Our results also indicate that the hole affinity of these regions is higher than that of B acceptors. Additionally, the bond distortion increases with the number of holes localized on it, independently if they come from B atoms or from charge modifications in the undoped a-Si cell. We have studied the EDOS of the configurations of Fig. 1, which are represented in Fig. 2. When the B atom is far from the distorted region 关Fig. 1共a兲兴, the EDOS 关Fig. 2共a兲兴has a shallow state near the top of the valence band. The position of the Fermi level indicates that the added hole is at the state associated with that peak. The same comment holds true for the case of placing the B atom at the distorted region 关Fig. 2共b兲兴. Nevertheless, the combination of the acceptor nature of the B atom with the hole affinity of the distorted region results in the stronger localization of the hole around the B atom 关Fig. 1共b兲兴. In both of the previous cases there is a good agreement with the EDOS of the a-Si cell positively charged 共specially when the B atom is far from the trapping region兲, which also has a peak near the valence-band edge 共VBE兲. When there are two B atoms in the a-Si cell 关Fig. 1共c兲兴, the EDOS 关Fig. 2共c兲兴shows a midgap peak. Since the Fermi level is at the VBE, the two holes are at the states associated with that peak. A very similar EDOS is obtained for the undoped a-Si cell when two holes are added to it. In Fig. 2共d兲we compare the EDOS of the neutral undoped a-Si cell, with that of a B-doped a-Si cell with negative charge 关in particular with the B atom at the same position as in Fig. 1共a兲兴, showing a very good agreement. Thus, in all cases the doped and undoped a-Si cells with the same total number of electrons have a very similar EDOS. From these results we conclude that there is a hole trap 共HT兲in the a-Si cell, which is associated with a region with highly distorted bond angles and captures holes provided by B atoms. Furthermore, its energy level changes its position in the gap according to its occupancy. When the HT is not occupied by holes, its energy level is stuck to the valence FIG. 1. 共Color online兲Hole spatial localization in 64-atom cells with 共a兲a B atom far from the HT region, 共b兲a B atom at the HT, and 共c兲two B atoms far from the HT, 共d兲as well as in a positively charged undoped cell. The dark shadowed areas show the isosurface at 50% of the maximum hole density. B atoms are black and marked by arrows. Si atoms are white and red 共gray兲. The red Si atoms indicate the position of the HT. BRIEF REPORTS PHYSICAL REVIEW B 81, 033203 共2010兲 033203-2 band. As one or two holes are captured, the level goes deeper and deeper in the gap. We have checked that, in contrast, the addition of one or two electrons 关共a-Si64兲−1 and 共a-Si63B兲−2 cells兴produce neither gap states nor relevant changes in the EDOS 共not shown兲. We have evaluated the hole binding energy, Eb, for the different changes in the HT occupancy as Eb +/0=ET 0−EVBE 0−ET +,共1兲 Eb ++/+=ET +−EVBE +−ET ++,共2兲 where ETis the total energy and EVBE is the energy of an electron at the VBE when the HT has no holes 共0兲, one 共+兲 or two holes 共++兲.Ebturns to be the effective activation energy for hole conduction. It is noteworthy that, due to atomic rearrangements when adding/removing holes, Ebcannot be simply calculated as the energy difference of the EDOS peaks to the VBE. The obtained energies for the undoped cell are Eb +/0=0.16 eV and Eb ++/+=0.29 eV. In a-Si cells with one B atom, the energies are Eb +/0 =0.15⫾0.03 eV and Eb ++/+=0.27⫾0.07 eV, which are comparable with those of the undoped a-Si cell. In the case of Fig. 1共c兲, we found Eb +/0=0.13 eV and Eb ++/+=0.20 eV, which are slightly lower than in the previous cases. This difference might be due to rearrangements when relaxing the cell with two B atoms since they have shorter bond lengths. In any case, Ebincreases with the occupancy of the HT. The good agreement in Ebfor the doped and undoped a-Si cells indicates that it is controlled by the HT and not by the B atoms. In the 216-atom cell we also found that holes provided to the sample 共by modifying the charge state or by replacing one or two Si atoms at different positions of the cell by B兲 were localized in a region associated to highly distorted bond angles, which also acts as a HT. These findings were confirmed by the analysis of the EDOS since the holes were at the states associated with the HT. In addition, we have found that Eb=0.12 eV for the doped and undoped 216-atom cells, which also indicates that the binding energy is controlled by the HT. According to these results, we schematically show in Fig. 3the effect of the HT in the B doping of a-Si. In an ideal scenario B atoms would have associated a shallow level near the VBE, and they would release easily their hole to the valence band. However, this does not occur when HTs are present since they capture the holes provided by B atoms. Once a hole is captured, Ebincreases from some meV 共supposing a shallow level for B atoms兲to ⬃0.15 eV. If the B atom is at the HT, the hole has a stronger spatial localization. For high B concentration, two holes are trapped and Ebis higher, ⬃0.3 eV. This picture helps to understand the role of HTs on B doping in a-Si. B atoms can behave as acceptors in the sense of providing the amorphous matrix with holes, but they are ineffective in doping since the HTs capture the available holes. The other appealing feature is that as holes are captured into these traps, Ebincreases. Hence, a-Si exhibits a “self-trapping” behavior for holes through these HTs, with higher hole affinity when holes are already trapped. This can contribute to increase the activation energy for conduction at high B concentration.5 We have also analyzed the energetics of B atoms by calculating their energy, ␧B, at the 64 different positions in the 64-atom cell as ␧B=Etot关共a-Si63B兲−兴−63 64Etot关共a-Si64兲0兴.共3兲 We have considered negative charged cells 关共a-Si63B兲−兴to minimize the distortion induced by the capture of holes at the HT. The results with neutral cells 关共a-Si63B兲0兴are qualitatively similar but with higher dispersion. We found that when B atoms replace Si atoms with shorter Si-Si bonds, the resulting B-Si bonds are shorter and energetically more favorable, as shown in Fig. 4共a兲. In Fig. 4共b兲we show the distance -2 -1.5 -1 -0.5 0 0.5 1 1. 5 (a-Si63B)- (a-Si64)0 d) (a-Si62B2)0 (a-Si64)++ c) (a-Si63B)0 (a-Si64)+ b) Ener gy (eV) Electronic Density of States (a-Si63B)0 (a-Si64)+ a) FIG. 2. 共Color online兲关共a兲–共c兲兴 EDOS of the corresponding B configurations of Fig. 1, together with EDOS of the undoped cell with the same number of electrons. 共d兲EDOS of the neutral undoped cell, together with the EDOS of a B-doped a-Si cell with negative charge where the B atom is at the same position as in Fig. 1共a兲. The origin of energies is at the conduction-band edge 共CBE兲 for convenience. The Fermi levels are indicated by vertical dashed lines. The shadowed area schematically shows the electronic filling. B E V B E I d e a l B i n a - S i ( B ) -B a t H T ( H T ) + ( B ) - H o l e t r a p & B d o p i n g ( B ) - ( H T ) + + ( B ) - H T & h i g h B d o p i n g FIG. 3. 共Color online兲Band scheme showing the effect of the studied HT in the B doping of a-Si 共see text for details兲. BRIEF REPORTS PHYSICAL REVIEW B 81, 033203 共2010兲 033203-3 of B atoms to the HT as a function of the average B bond length. We define the HT position as the center of mass of the red atoms of Fig. 1. B atoms placed at the red positions of Fig. 1are labeled as “At HT,” B atoms at the first bondconnected positions as “first neighbor,” etc. Diamonds represent the average on the distances of the groups. We found that, despite the scattering of the data, the distortion around the HT results, on average, in shorter B bond lengths and hence in B configurations with lower ␧B. Then, B atoms could be retained preferentially near the HT affecting their diffusion through the a-Si matrix. In conclusion, we have found that, even in the most ideal situation of substitutional B doping of fourfold coordinated a-Si, the doping efficiency is highly influenced by the presence of HTs in the amorphous matrix associated to distorted bond angles. These HTs capture the available holes. Hence, the effective activation energy for hole conduction is not the ionization energy of the B atom but the binding energy of the hole to the HT. This binding energy depends on the HT occupancy, increasing with the number of trapped holes. The case of two holes at the HT 共high B concentration兲results in a midgap level without the intervention of dangling bonds. In addition, the distortion induced by the HT results, on average, in shorter B bond lengths at its vicinity, which also results in B configurations with lower energy. This work has been partially funded by the Ohio Supercomputer Center 共computer time兲; the Spanish DGI under Grants No. TEC2008-0609 共I.S., L.P., and L.A.M.兲and No. TEC2008-05301 共P.C.兲; the ARO under Grant No. MURI W91NF-06-2-0026 共D.A.D.兲; and the Ohio State University Center for Emergent Materials 共a NSF MRSEC; Grant No. DMR-0820414兲共W.W.兲. *[email protected] 1R. A. 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Furthmüller, Comput. Mater. Sci. 6,15共1996兲; Phys. Rev. B 54, 11169 共1996兲. 14J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 共1992兲. 15F. Wooten, K. Winer, and D. Weaire, Phys. Rev. Lett. 54, 1392 共1985兲. 16L.-W. Wang, J. Appl. Phys. 105, 123712 共2009兲. 0 2 4 6 8 2 2.04 2.08 2.12 2.16 Avera g e B bond len g th (Å) −2 −1.6 −1.2 −0.8 − 0 . 4 Distance to the HT (Å) εB(eV) a) b) At HT 1st neigh. 2nd neigh. >2nd neigh. FIG. 4. 共Color online兲共a兲Energy of B atoms as a function of the average B bond length. The dashed line is a fit to the data. 共b兲 Distance of B atoms to the HT as a function of their average bond length. Diamonds are the average value of the groups, and the dashed line is to guide the eye. BRIEF REPORTS PHYSICAL REVIEW B 81, 033203 共2010兲 033203-4