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Binding of hydrogen to phosphorus dopant in phosphorus-doped diamond surfaces: A density functional theory study
Applied Surface Science 471 (2019) 309–317
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Full Length Article
Binding of hydrogen to phosphorus dopant in phosphorus-doped diamond surfaces: A density functional theory study ⁎
⁎
T
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Wei Shena,b, Shengnan Shena,b,c, , Sheng Liua,b,c, , Hui Lia,b,c, , Siyuan Nieb, Yuanhui Panb, Zhiqiang Tianb, Qifan Lib a
Research Institute of Wuhan University in Shenzhen, Wuhan University, Shenzhen 518057, China School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China c The Institute of Technological Sciences, Wuhan University, Wuhan 430072, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: P-doped diamond Density functional theory Hydrogen P–H complex
Although phosphorus is an n-type donor in diamond, H impurities can bind to and passivate P. Here, H binding to a P dopant in both diamond (0 0 1) and (1 1 1) surfaces is investigated by density functional theory. The energy calculations reveal the most stable P–H complex structures for each P-doped position. P–H binding energies are the lowest for the second P doped C layer among those for four investigated P-doped C layers. H migration from on-surface to P in the second C layer is exothermic, with an energy barrier of zero, whereas that from on-surface to P below the second C layer is endothermic, with an energy barrier greater than 0.95–7.09 eV. Thus, both of binding energy and migration calculations imply that P–H complex is more likely to form when P is doped in the second C layer than when P is doped below the second C layer. Moreover, H migration energy barrier from on-surface to P below the second C layer in the (1 1 1) surface is at least 0.85 eV greater than that in the (0 0 1) surface, which indicates that P–H complex is less likely to form in (1 1 1) surface than in (0 0 1) surface.
1. Introduction Because diamond possesses unusual physical properties, including a large bandgap (5.47 eV), high thermal conductivity (20 W cm−1 K−1) [1], and high mobility for both holes and electrons (∼2500 cm2 V−1 s−1) [2], it is expected to be a next-generation semiconductor material for high power, high frequency, and high-temperature electronic devices. Achieving efficient n-type doping in diamond is one of the important issues facing the development of such applications. Researchers have primarily focused on Nitrogen (N), Sulphur (S), and phosphorus (P) doping at substitutional sites in diamond. N has a deep donor level with an activation energy of 1.7 eV, which makes it useless for room-temperature semiconductor devices [3]. The activation energy of electrical conduction in S-doped diamond has been reported to be 0.19–0.33 eV [4]. The theoretical donor level of neutral S has been demonstrated to be 0.16 eV [5]. However, the relative energy for the incorporation of S into diamond is 9.4 eV, whereas that of P is 4.2 eV; thus, S exhibits much lower solubility into bulk diamond than P [6]. Comparatively, the calculated donor level of P is 0.6 eV [7] (lower than the 1.7 eV of N), and it has higher solubility than S, which implies that P is a more appropriate n-type donor than N or S. ⁎
Growth of P-doped diamond by chemical vapor deposition (CVD) has become a well-established field over the past two decades. P-doped diamond was first experimentally demonstrated on the (1 1 1) surface with a donor level of 0.43 eV in 1997 [8]. P dopant has also been successfully incorporated into diamond in epitaxial growth on the (0 0 1) surface [9,10]. The room temperature resistivity is 120–150 Ω cm for 1.5 × 1020 P/cm3 on the (1 1 1) surface [11] and 5.0 × 106 Ω·cm for 5.1 × 1016 P/cm3 on the (0 0 1) surface [12]. The P donor fraction (i.e., the ratio between the net P concentration acting as donors and the incorporated P concentration) approaches 1 on the (1 1 1) surface [13] but is less than 0.65 on the (0 0 1) surface [14,15]. The high room-temperature resistivity for a P-doped diamond film and low P donor fraction are due to the high carrier compensation ratio. Theoretical studies have shown that the formation of P–H complex is one of the reasons for compensation of carriers [16–18]. Secondary-ion mass spectroscopy analysis has indicated that H exists on the P-doped diamond surfaces [16,19,20]. This residual H can be bound to P and passivate the P donor [20,21]. Hydrocarbons diluted with H2 as the raw material gas are generally used during diamond growth [20]; thus, these H atoms can migrate from the on-surface to the subsurface and bind to P atoms, leading to the formation of P–H complexes. However,
Corresponding authors. E-mail addresses: [email protected] (S. Shen), [email protected] (S. Liu), [email protected] (H. Li).
https://doi.org/10.1016/j.apsusc.2018.12.018 Received 3 September 2018; Accepted 3 December 2018 Available online 03 December 2018 0169-4332/ © 2018 Elsevier B.V. All rights reserved.
Applied Surface Science 471 (2019) 309–317
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Table 1 Number of atomic carbon layers (n), k points set, and the sizes in the x-, y- and z-directions of the two slab models. Surface
n
k points set
Size (Å3)
(0 0 1) (1 1 1)
9 10
2×2×1 3×3×1
10.12 × 10.12 × 21.00 8.76 × 7.59 × 25.00
P–H complex structures and the H migration process in the diamond surface have not yet been investigated during diamond film growth, although the structures and formation energies of P–H complexes in bulk diamond have been studied by many researchers [15,16,18,22]. The mechanism of P–H complex formation in the diamond surface requires quantitative analysis, which is difficult to perform experimentally. The main purpose of the present study is to investigate binding of H to P dopant within both diamond (0 0 1) and (1 1 1) surfaces by density functional theory (DFT). The H-terminated (0 0 1)-2 × 1 and (1 1 1)1 × 1 surfaces are used to mimic the as-grown CVD diamond surfaces in this work, consistent with previous literatures [23,25], because these surfaces are most frequently observed in experiments involving diamond film growth [26–28]. The P dopant is substitutionally positioned in the second, third, fourth, or fifth Carbon (C) layer in diamond (0 0 1) and (1 1 1) surfaces. The structures of the P–H complexes and the binding energy of H to the P dopant in different positions within diamond (0 0 1) and (1 1 1) surfaces are obtained by geometry optimization and energy calculations. When the P dopant is in the second C layer, the energy barrier and reaction energy of H migrating from onsurface to P dopant are investigated by the method proposed by Ref. [24]. When the P dopant is in the third, fourth, or fifth C layer, the energy barrier and reaction energy of H migrating from on-surface to the P dopant are investigated by the complete linear synchronous transit and quadratic synchronous transit (LST/QST) method [29].
Fig. 2. Illustration of the simulated H absorption process. (The colored atoms are defined in Fig. 1.)
Fig. 3. Schematics of the stable P–H complex structures and corresponding H sites around P. (C, P, and H atoms are shown as gray, blue, and red circles, respectively.)
2. Calculation method The calculations in this work are performed using the program
Fig. 1. Slab models of the diamond (a) (0 0 1) and (b) (1 1 1) surfaces. (The colored atoms represent the positions of the P atoms.) 310
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Table 2 Structural data, bond populations, and atomic charges of P–H complexes in P-doped diamond surfaces; d0 refers to the bond length of P–H, and d1, d2, d3, and d4 are described in Fig. 2. Diamond surface
Doping carbon layer
Position of P
Position of H
Bond population of P–H
d0, d1, d2, d3, d4 (Å)
(0 0 1)
II III
V
A A B A B A
AB1 AB1 AB1 AB1 AB1 AB1
0.63 0.98 0.77 0.90 0.88 0.88
1.468, 1.309, 1.464, 1.336, 1.323, 1.325,
1.748, 1.714, 1.723, 1.698, 1.742, 1.704,
1.748, 1.714, 1.723, 1.698, 1.742, 1.720,
1.807, 1.764, 1.770, 1.702, 1.764, 1.730,
II III IV V
A A A A
AB1 AB1 AB1 AB1
0.57 0.91 0.89 0.89
1.504, 1.315, 1.322, 1.322,
1.715, 1.726, 1.710, 1.713,
1.715, 1.728, 1.710, 1.715,
1.723, 1.778, 1.724, 1.720,
IV
(1 1 1)
P atom charge
H atom charge
1.953 1.790 1.895 1.766 1.801 1.780
1.20 1.40 1.25 1.42 1.35 1.40
−0.22 −0.21 −0.25 −0.22 −0.22 −0.22
2.183 1.799 1.776 1.772
1.21 1.36 1.41 1.41
−0.26 −0.22 −0.23 −0.23
substituted in the first carbon layer, a P atom is bonded to three C atoms only. Therefore, the first P-doped C layer is excluded in this work. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [34] is used to optimize the geometric structure of a diamond surface. The convergence criterion of the inter-atomic forces is set to 0.03 eV/Å, and the energy of self-consistent calculation is 1.0 × 10−5 eV/atom. The lowest C and H layers are frozen during the optimization to simulate the constraint imposed by the bulk. Prior to the geometry optimization and energy calculations, a lattice constant of 0.3577 nm is determined through optimizing the diamond crystalline structure. This value is similar to the experimental value of 0.3567 nm [35]. To ensure the reliability of our results, H abstraction values on the (0 0 1) and (1 1 1) surfaces in the present study are calculated, as 6.06 eV and 5.85 eV, respectively, in agreement with previously reported theoretical values of 6.10 eV [36] and 4.90 eV [37], respectively. The binding energy of an H atom to a P dopant in the P-doped diamond surface is calculated using Eq. (1):
Fig. 4. Binding energy of P–H as a function of P-doped carbon layer in diamond (0 0 1) and (1 1 1) surfaces. (The P-doped positions are illustrated in Fig. 1.)
ΔEb = EP − H − EP − EH package CASTEP [30], which is based on DFT. A plane-wave basis is set and periodic boundary conditions are used to determine the Kohn–Sham ground state. In specific calculations, a spin-polarized general gradient approximation and the PW91 functional (Perdew-Wang) [31] for exchange correlation energy are used. The Brillouin zone is sampled with the Monkhorst–Pack k-points grid [32] in reciprocal space during self-consistent calculations to identify the electronic ground state. The detailed calculation parameters of slab models of both the diamond (0 0 1) and (1 1 1) surfaces are listed in Table 1; the cut-off energy is set to 280 eV. The choice of k-points set and cut-off energy parameters are selected on the basis of careful test calculations; higher values of these two parameters show an energy difference of only 1.2% in calculations of the H binding energy (Eq. (1)). Fig. 1 presents slab models of both diamond (0 0 1) and (1 1 1) surfaces. The Roman numerals II, III, IV, and V denote P dopant in the second, third, fourth, and fifth C layers, respectively, and the letters A and B denote the positions of P in each C layer. The periodic boundary conditions are used in the calculations. A large vacuum space (> 10 Å [33]) between the slabs (in the z-direction) is used to eliminate interslab interactions. Nine and ten C layers are sufficient to determine the H binding energy with sufficient accuracy for the (0 0 1) and (1 1 1) surfaces, respectively. A further increase in the number of C layers does not render any visible change in numerical value for the H binding energy by less than 0.9%. The various substitutional positions for P are also showed in Fig. 1. Substitutional P dopants in the second, third, fourth, and fifth C layers are investigated in this work. For the (0 0 1) surface, there are one substitutional P position in the second and fifth C layer and two positions in the third and fourth C layer. Because of the high symmetry of the (1 1 1) surface, only one substitutional P position in each C layer is investigated. According to the definition of the P–H complex [22], a P atom is bonded to four C atoms and one H atom. When P dopant is
(1)
where EP–H is the total energy of the diamond surface with a P–H complex, EP is the total energy of the P-doped diamond surface without H, and EH is the energy of the H atom. For the P dopant in the second C layer, the energy barrier of H absorption reaction is estimated by the method in Ref. [24]. The H atom is approached in small steps toward the P dopant in the second C layer, as simulated in Fig. 2. The introduced H atom is frozen in varying sites along the reaction path and finally bonded to P atom, and the rest of the structure is relaxed. The energy barrier can be estimated from the energy profile, which is obtained by the energy of each step as an H atom approaches. For P doped in the third, fourth, or fifth C layer, the migration barrier and reaction path of H atoms from on-surface to the P dopant are calculated using the LST/QST method [29]. 3. Results and discussions It is very difficult to experimentally observe the P–H complex structure and its formation process in diamond surface. Theoretical DFT calculations are therefore very useful. In the present study, the P dopants are substitutionally positioned into C layers II, III, IV, and V, and then the stable P–H complex structures and binding energy are calculated. The formation process of the P–H complex can be considered as the process of H migrating from on-surface to subsurface and finally binding with P dopant in each C layer. 3.1. P–H complex structure and binding energy To obtain P–H complex structures in the diamond surface, the H atom is initially placed at different sites around the P dopant, and then the P–H complex structures and corresponding H sites are obtained after geometry optimization. Schematics of P–H complex structures are 311
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Fig. 5. Schematics of stable positions of H on the diamond (a) (0 0 1) and (b) (1 1 1) surfaces.
there are correspondingly two P–H complex structures for each P position. The P–H complex has a lower energy when H is at the AB1 site than when H is at the AB2 site. This result implies that the P–H complex is most stable when H is at the AB1 site. The P–H complex structures with H atoms at AB1 sites are the main focus here; the calculated structural data, bond populations, and atomic charges of these P–H complexes are summarized in Table 2. The P-C bond length d4 is slightly elongated by the incorporation of H, and it is largest among d1, d2, d3, and d4, which is the same as trend for the bond lengths of the P–H complex structures in bulk diamond [22]. The charges of the P and H atoms in the P–H complex are positive and negative, respectively, which can be explained by the higher Pauling electronegativity of H (electronegativity 2.20) compared with that of P (electronegativity 2.19) [3]. The binding energies of P–H as a function of the P-doped C layer number of the P position, are calculated; the results are shown in Fig. 4. A negative binding energy value means that the binding of H to P is exothermic. The P–H binding energy value is lowest for a P dopant at the II-A site. Thus, H binding to a P dopant in the second C layer is energetically most favorable, which implies that the P–H complex is most stable for P doped into the second layer. The binding energy should mainly include two contributions: (i) the energy of the
shown in Fig. 3. The H of P–H complex has three different sites: antibonded (AB), bond-center (BC) and cross-line (CL) sites. C1, C2, C3, and C4 are C atoms near the P atom, and d1, d2, d3, and d4 represent the bond length between the C atom and P atom. α1 is the bond angle between the P–H bond and the d4 bond. The BC site is between the C and P atom, the AB site is opposite the C4 atom along the d4 axis, and the CL site is near the intersecting line between the two planes (one plane consists of C1, C2, and P sites, the other plane consists of C3, C4, and P sites). We find that the P–H complex structures and corresponding H sites in the diamond surface model are slightly different but similar to those in bulk diamond; specifically, the AB, BC, and CL sites in diamond surface are similar to the antibonding, bond center, and 0 0 1 sites in bulk diamond [38], respectively. For example, for the AB site of H around P within the second C layer in the diamond (0 0 1) surface, α1 is 178.5°, whereas α1 is 180° in bulk diamond. Our energy calculations reveal that H at the AB site has the lowest energy among H atoms at the three sites for P–H complex in each of the four C layers. This result is consistent with the previously reported conclusion that the P–H complex has the most stable structure when H is at anti-bonded site in bulk diamond [38]. Two stable AB sites of H around each P position (these two sites are labeled as AB1 and AB2 sites) are found by energy calculation, and 312
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fixed site and the P dopant in the (0 0 1) surface. The bond population value between these two atoms is positive (0.07), indicating an electron orbital overlap. This value strongly supports our hypothesis that no stable H site exists above the P dopant in the second C layer and that the barrier energy value for the binding of H to P dopant in the second C layer within the diamond (0 0 1) surface is zero. Further calculations reveal that the energy barrier value of H migrating to a P dopant is zero within the (1 1 1) surface. Therefore, P–H complex is easy to form, when the P dopant is in the second C layer within the (0 0 1) or (1 1 1) surface. The energy profiles for the H migration path from on-surface to a P dopant below the second C layer in diamond (a–e) (0 0 1) and (f–h) (1 1 1) surfaces are displayed in Fig. 7. The relaxed surface models in Fig. 7 are the local structures containing the P dopant. The labels below the local structures contain the information related to the P and H sites. For example, (0 0 1)-III-A-AB1 represents a P dopant at position A of the third C layer with H at the AB1 site in the (0 0 1) surface. The P-doped diamond surfaces with H at the surface stable site are chosen as the initial states, and the obtained P-doped diamond surfaces with H at the AB1 site (listed in Table 2) are chosen as the final states for our migration calculations. The (0 0 1)-IV-B-AB2 site is a local energy minimum site between the (0 0 1)-IV-B-S2 and (0 0 1)-IV-B-AB1 sites in Fig. 7(d). The (1 1 1)-III-A-CL1 site is a local energy minimum site between the (1 1 1)-III-A-S1 and (1 1 1)-III-A-AB1 sites in Fig. 7(f), and CL1 refers to a CL site of H around P. The (1 1 1)-IV-A-AB2 site is a local energy minimum site between the (1 1 1)-IV-A-S1 and (1 1 1)-IV-A-AB1 sites Fig. 7(g). The (1 1 1)-V-A-CL1 site is a local minimum site between the (1 1 1)-V-A-S1 and (1 1 1)-V-A-AB1 sites in Fig. 7(h). For the diamond (0 0 1) or (1 1 1) surface, the reaction energy value is positive for H migration from on-surface to a P dopant below the second C layer and its energy barrier value is greater than 0.95 eV–7.09 eV, which implies that formation of the P–H complex is difficult for P dopants below the second C layer. Comparatively, the corresponding reverse reaction energy value is negative for the H migration from a P dopant below the second C layer to on-surface and its energy barrier is relatively lower, which implies that the H atom of the P–H complex is more likely to migrate from the AB1 site below the second C layer to on-surface than from on-surface to a P dopant below the second C layer. Reaction energy values for the migration of H to a P dopant below the second C layer are positive (endothermic reaction), which is inconsistent with the negative binding energy values of P–H (exothermic reaction). This can be explained by that the P–H binding energy consists of energy of H absorption onto the surface and the energy of the H migration reaction, and the energy of H absorption onto the surface is obviously negative. For the diamond (0 0 1) surface, the energy barrier value (0.95 eV) is the lowest for the path (0 0 1)-III-B-S2 to (0 0 1)-III-B-AB1 and is largest (5.58 eV) for the path (0 0 1)-IV-A-S1 to (0 0 1)-IV-A-AB1. This result is consistent with the binding energy being largest for a P dopant at the (0 0 1)-IV-A site. For the diamond (1 1 1) surface, the energy barrier value is lowest (6.43 eV) for the path (1 1 1)-IV-A-S1 to (1 1 1)IV-A-AB1 and largest (7.09 eV) for the path (1 1 1)-V-A-S1 to (1 1 1)-VA-AB1. The energy barrier value for H migrating from on-surface to a P dopant below the second C layer is at least 0.85 eV larger for each Pdoped layer in the diamond (1 1 1) surface than for each P-doped layer in the (0 0 1) surface. This result indicates that the P–H complex is less likely to form for the diamond (1 1 1) surface than for the (0 0 1) surface when a P dopant is in the third, fourth, or fifth C layer during the diamond film growth. Our calculations predict that the energy barrier for H migration from on-surface to subsurface is greater than 4.5 eV ((0 0 1) surface) or 7 eV ((1 1 1) surface) for a P dopant below the fifth C layer. Thus, H migration is difficult. Cases where a P dopant is below the fifth C layer are therefore excluded in the present study.
Fig. 6. The electron density difference map showing the interaction between the fixed H atom and the P dopant. (Blue indicates where charge is lost, red indicates where charge is accumulated, and yellow indicates where charge doesn’t change. The colored atoms are defined in Fig. 1.)
interaction between an H atom and a P dopant in the diamond surface and (ii) the deformation energy of the P-doped diamond surface. A greater interaction between the H atom and P dopant in the diamond surface or less deformation of the P-doped diamond surface, results in lower binding energy. As shown in Table 2, for both the (0 0 1) and (1 1 1) surfaces, the P–H bond populations for P dopants in the third, fourth, and fifth C layers are larger than those for P dopants in the second C layer, which indicates that P dopant and H atom interact more strongly. Therefore, higher H binding energies may be explained by H binding leading to relatively larger geometric deformation for P dopants below the second C layer than for P dopants in the second C layer.
3.2. Energy profiles of H migration The gas chamber contains a large amount of H atoms, and the H atoms above the surface are the main source of H for forming P–H complexes in the subsurface. The stable P–H complex for each P position in (0 0 1) and (1 1 1) surface are obtained in the previous section. In this section, we calculate the energy profiles of H migrating from onsurface to P dopants to investigate the formation process of P–H complexes. For P dopant in third, fourth, or fifth C layer, there are two stable sites of H above the P dopant on diamond (0 0 1) surface, and one on (1 1 1) surface, as shown in Fig. 5. For P at the (0 0 1)-III-A or (1 1 1)-IIIA position, the S1 site of H is a highly symmetric position. For P at the (0 0 1)-III-B, the S2 site of H is a highly symmetric position. For P at the (0 0 1)-IV-A, (0 0 1)-V-A, (1 1 1)-IV-A, or (0 0 1)-V-A position, the stable site for H on the surface is not exactly at but near a highly symmetric position; the specific stable positions of H are determined through geometry optimization calculations. Numerous other stable sites for H exist on the surface but are excluded in this work because H migration barriers from these sites to P dopant sites in the subsurface are higher than those from the stable sites in Fig. 5 to P dopant sites in the subsurface. For P dopant in the second C layer within the diamond (0 0 1) surface, no stable site of H exists above the P dopant and the energy barrier value for H migrating to the P dopant is zero. We calculated the stable site for H on the pure diamond (0 0 1) surface, and then substituted a P dopant for a C atom in the second C layer while leaving the H atom at the stable site fixed during relaxation. The H electron density difference map in Fig. 6 shows a strong interaction between the H at the 313
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Fig. 7. Energy profiles for H migration from the on-surface to the subsurface in diamond (a–e) (0 0 1) and (f–h) (1 1 1) surface. (Energy unit: eV. The colored atoms are defined in Fig. 1.)
314
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Fig. 7. (continued)
implies that fewer P donors could be passivated and more P atoms could act as donors in the (1 1 1) surface than in the (0 0 1) surface, consistent with the experimental finding of a lower P donor fraction in the (0 0 1) surface than in the (1 1 1) surface [13–15]. Some researchers have speculated that the (0 0 1) surface is preferred for future applications, because the room temperature Hall mobility of the diamond (0 0 1) surface is four times greater than that of the diamond (1 1 1) surface [12,15]. However, our results suggest that P-doped diamond should be fabricated on the (1 1 1) surface because the P–H complex is less likely to form for a P dopant below the second C layer in (1 1 1) surface than for a P dopant below the second C layer in the (0 0 1) surface.
3.3. Discussions The formation of P–H complex is one of the reasons for compensation of carriers in diamond film [16–18]. Thus, the P–H complexes should be eliminated during the diamond film growth, to obtain a highquality P-doped diamond film. Among the four P-doped C layers, a P–H complex is most likely to form when P dopant is in the second C layer. During the growth of a diamond film, if P–H complexes are not eliminated, a large amount of P–H complexes in the second carbon layer will be brought into bulk diamond. Our results suggest that H atoms should be prevented from binding to P when P dopant is present in the second C layer. When a P–H complex forms in the third, fourth, or fifth carbon layer, H migration from the subsurface to on-surface is an exothermic reaction. Therefore, the P–H complex could be removed by imposing an external energy field (such as an increase in temperature) to increase the tunneling probability of H migration to on-surface when a P–H complex is in the third, fourth, or fifth C layer. When a P dopant is in the third, fourth, or fifth C layer during the diamond film growth, a P–H complex is less likely to form in the diamond (1 1 1) surface than in the (0 0 1) surface. This result further
4. Conclusions H-terminated (0 0 1) and (1 1 1) diamond models are built to mimic the as-grown CVD diamond surface. H binding to a P dopant in diamond (0 0 1) and (1 1 1) surfaces is systematically calculated by DFT. The following conclusions are drawn from the results: (1) P–H complex structures for each P dopant positions in diamond surfaces are obtained. For each P dopant, the most stable P–H 315
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References
complex forms when H occupies the AB1 site around the P dopant. There are AB, BC, and CL sites of H around P dopant in P–H complex structure, and the P–H complex has the lowest energy when H occupies the AB site among these three sites. Moreover, for each P position, there are two AB sites (AB1 and AB2 sites) of H. The P–H complex has a lower energy when H occupies the AB1 site rather than the AB2 site, which implies that P–H complex is most stable when H occupies the AB1 site. (2) The stability of P–H complexes for each P-doped position in diamond (0 0 1) and (1 1 1) surfaces is compared. For P doped in the second C layer, the P–H binding energy values are −4.61 eV and −4.44 eV in the (0 0 1) and (1 1 1) surfaces, respectively, which are the lowest among the four P-doped C layers. This implies that the P–H complex is more energetically stable when P is doped within the second C layer than when P is doped in other C layers. (3) The H migration process and formation mechanism of P–H complexes in diamond surfaces are clarified. For P doped in the second C layer, H migration from on-surface to the P dopant is an exothermic process and its energy barrier is zero. For P doped below the second C layer, H migration from on-surface to the P dopant is an endothermic reaction and its energy barrier is greater than 0.95–7.09 eV. This finding indicates that a P–H complex is more likely to form when P is doped within the second C layer than when P is doped below the second C layer. Comparatively, the corresponding reverse reaction is exothermic for the H migration from the P dopant below the second layer to on-surface. This result implies that an H atom of the P–H complex is more likely to migrate from the AB1 site below the second C layer to on-surface than from on-surface to a P dopant below the second C layer. (4) P–H complex is more likely to form for the diamond (0 0 1) surface than for the diamond (1 1 1) surface when the P dopant is in the third, fourth, or fifth C layer during the growth of a diamond film. The H migration energy barrier from on-surface to a P dopant below the second C layer is at least 0.85 eV greater for each of the P-doped C layers in the diamond (1 1 1) surface than for each of the P-doped layers in the diamond (0 0 1) surface. It also indicates that fewer P donors could be passivated in the (0 0 1) surface than in the (1 1 1) surface.
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The research presented here provides detailed information about the structures and formation process of P–H complexes during diamond film growth. Furthermore, it provides guidance on how to eliminate P–H complex formation for fabricating a high-quality P-doped diamond film. Specifically, (i) to avoid the formation of P–H complexes from the outset, H atoms should be prevented from binding with P dopant in the second C layer. (ii) Ideally, P–H complexes could be removed by imposing an external energy field (such as an increase in temperature) to promote H migrating from subsurface to on-surface when the P dopant is in the third, fourth, or fifth C layer. (iii) P-doped diamond should be fabricated on the (1 1 1) surface, because the P–H complex is less likely to form for P dopant atoms below the second C layer in the (1 1 1) surface than for P dopant atoms below the second C layer in the (0 0 1) surface.
Acknowledgements This work is supported by the International Cooperation Research Project of Shenzhen (GJHZ20180413182004161) and the National Natural Science Foundation of China (51727901).
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2018.12.018. 316
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Full Length Article
Binding of hydrogen to phosphorus dopant in phosphorus-doped diamond surfaces: A density functional theory study ⁎
⁎
T
⁎
Wei Shena,b, Shengnan Shena,b,c, , Sheng Liua,b,c, , Hui Lia,b,c, , Siyuan Nieb, Yuanhui Panb, Zhiqiang Tianb, Qifan Lib a
Research Institute of Wuhan University in Shenzhen, Wuhan University, Shenzhen 518057, China School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China c The Institute of Technological Sciences, Wuhan University, Wuhan 430072, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: P-doped diamond Density functional theory Hydrogen P–H complex
Although phosphorus is an n-type donor in diamond, H impurities can bind to and passivate P. Here, H binding to a P dopant in both diamond (0 0 1) and (1 1 1) surfaces is investigated by density functional theory. The energy calculations reveal the most stable P–H complex structures for each P-doped position. P–H binding energies are the lowest for the second P doped C layer among those for four investigated P-doped C layers. H migration from on-surface to P in the second C layer is exothermic, with an energy barrier of zero, whereas that from on-surface to P below the second C layer is endothermic, with an energy barrier greater than 0.95–7.09 eV. Thus, both of binding energy and migration calculations imply that P–H complex is more likely to form when P is doped in the second C layer than when P is doped below the second C layer. Moreover, H migration energy barrier from on-surface to P below the second C layer in the (1 1 1) surface is at least 0.85 eV greater than that in the (0 0 1) surface, which indicates that P–H complex is less likely to form in (1 1 1) surface than in (0 0 1) surface.
1. Introduction Because diamond possesses unusual physical properties, including a large bandgap (5.47 eV), high thermal conductivity (20 W cm−1 K−1) [1], and high mobility for both holes and electrons (∼2500 cm2 V−1 s−1) [2], it is expected to be a next-generation semiconductor material for high power, high frequency, and high-temperature electronic devices. Achieving efficient n-type doping in diamond is one of the important issues facing the development of such applications. Researchers have primarily focused on Nitrogen (N), Sulphur (S), and phosphorus (P) doping at substitutional sites in diamond. N has a deep donor level with an activation energy of 1.7 eV, which makes it useless for room-temperature semiconductor devices [3]. The activation energy of electrical conduction in S-doped diamond has been reported to be 0.19–0.33 eV [4]. The theoretical donor level of neutral S has been demonstrated to be 0.16 eV [5]. However, the relative energy for the incorporation of S into diamond is 9.4 eV, whereas that of P is 4.2 eV; thus, S exhibits much lower solubility into bulk diamond than P [6]. Comparatively, the calculated donor level of P is 0.6 eV [7] (lower than the 1.7 eV of N), and it has higher solubility than S, which implies that P is a more appropriate n-type donor than N or S. ⁎
Growth of P-doped diamond by chemical vapor deposition (CVD) has become a well-established field over the past two decades. P-doped diamond was first experimentally demonstrated on the (1 1 1) surface with a donor level of 0.43 eV in 1997 [8]. P dopant has also been successfully incorporated into diamond in epitaxial growth on the (0 0 1) surface [9,10]. The room temperature resistivity is 120–150 Ω cm for 1.5 × 1020 P/cm3 on the (1 1 1) surface [11] and 5.0 × 106 Ω·cm for 5.1 × 1016 P/cm3 on the (0 0 1) surface [12]. The P donor fraction (i.e., the ratio between the net P concentration acting as donors and the incorporated P concentration) approaches 1 on the (1 1 1) surface [13] but is less than 0.65 on the (0 0 1) surface [14,15]. The high room-temperature resistivity for a P-doped diamond film and low P donor fraction are due to the high carrier compensation ratio. Theoretical studies have shown that the formation of P–H complex is one of the reasons for compensation of carriers [16–18]. Secondary-ion mass spectroscopy analysis has indicated that H exists on the P-doped diamond surfaces [16,19,20]. This residual H can be bound to P and passivate the P donor [20,21]. Hydrocarbons diluted with H2 as the raw material gas are generally used during diamond growth [20]; thus, these H atoms can migrate from the on-surface to the subsurface and bind to P atoms, leading to the formation of P–H complexes. However,
Corresponding authors. E-mail addresses: [email protected] (S. Shen), [email protected] (S. Liu), [email protected] (H. Li).
https://doi.org/10.1016/j.apsusc.2018.12.018 Received 3 September 2018; Accepted 3 December 2018 Available online 03 December 2018 0169-4332/ © 2018 Elsevier B.V. All rights reserved.
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Table 1 Number of atomic carbon layers (n), k points set, and the sizes in the x-, y- and z-directions of the two slab models. Surface
n
k points set
Size (Å3)
(0 0 1) (1 1 1)
9 10
2×2×1 3×3×1
10.12 × 10.12 × 21.00 8.76 × 7.59 × 25.00
P–H complex structures and the H migration process in the diamond surface have not yet been investigated during diamond film growth, although the structures and formation energies of P–H complexes in bulk diamond have been studied by many researchers [15,16,18,22]. The mechanism of P–H complex formation in the diamond surface requires quantitative analysis, which is difficult to perform experimentally. The main purpose of the present study is to investigate binding of H to P dopant within both diamond (0 0 1) and (1 1 1) surfaces by density functional theory (DFT). The H-terminated (0 0 1)-2 × 1 and (1 1 1)1 × 1 surfaces are used to mimic the as-grown CVD diamond surfaces in this work, consistent with previous literatures [23,25], because these surfaces are most frequently observed in experiments involving diamond film growth [26–28]. The P dopant is substitutionally positioned in the second, third, fourth, or fifth Carbon (C) layer in diamond (0 0 1) and (1 1 1) surfaces. The structures of the P–H complexes and the binding energy of H to the P dopant in different positions within diamond (0 0 1) and (1 1 1) surfaces are obtained by geometry optimization and energy calculations. When the P dopant is in the second C layer, the energy barrier and reaction energy of H migrating from onsurface to P dopant are investigated by the method proposed by Ref. [24]. When the P dopant is in the third, fourth, or fifth C layer, the energy barrier and reaction energy of H migrating from on-surface to the P dopant are investigated by the complete linear synchronous transit and quadratic synchronous transit (LST/QST) method [29].
Fig. 2. Illustration of the simulated H absorption process. (The colored atoms are defined in Fig. 1.)
Fig. 3. Schematics of the stable P–H complex structures and corresponding H sites around P. (C, P, and H atoms are shown as gray, blue, and red circles, respectively.)
2. Calculation method The calculations in this work are performed using the program
Fig. 1. Slab models of the diamond (a) (0 0 1) and (b) (1 1 1) surfaces. (The colored atoms represent the positions of the P atoms.) 310
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Table 2 Structural data, bond populations, and atomic charges of P–H complexes in P-doped diamond surfaces; d0 refers to the bond length of P–H, and d1, d2, d3, and d4 are described in Fig. 2. Diamond surface
Doping carbon layer
Position of P
Position of H
Bond population of P–H
d0, d1, d2, d3, d4 (Å)
(0 0 1)
II III
V
A A B A B A
AB1 AB1 AB1 AB1 AB1 AB1
0.63 0.98 0.77 0.90 0.88 0.88
1.468, 1.309, 1.464, 1.336, 1.323, 1.325,
1.748, 1.714, 1.723, 1.698, 1.742, 1.704,
1.748, 1.714, 1.723, 1.698, 1.742, 1.720,
1.807, 1.764, 1.770, 1.702, 1.764, 1.730,
II III IV V
A A A A
AB1 AB1 AB1 AB1
0.57 0.91 0.89 0.89
1.504, 1.315, 1.322, 1.322,
1.715, 1.726, 1.710, 1.713,
1.715, 1.728, 1.710, 1.715,
1.723, 1.778, 1.724, 1.720,
IV
(1 1 1)
P atom charge
H atom charge
1.953 1.790 1.895 1.766 1.801 1.780
1.20 1.40 1.25 1.42 1.35 1.40
−0.22 −0.21 −0.25 −0.22 −0.22 −0.22
2.183 1.799 1.776 1.772
1.21 1.36 1.41 1.41
−0.26 −0.22 −0.23 −0.23
substituted in the first carbon layer, a P atom is bonded to three C atoms only. Therefore, the first P-doped C layer is excluded in this work. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [34] is used to optimize the geometric structure of a diamond surface. The convergence criterion of the inter-atomic forces is set to 0.03 eV/Å, and the energy of self-consistent calculation is 1.0 × 10−5 eV/atom. The lowest C and H layers are frozen during the optimization to simulate the constraint imposed by the bulk. Prior to the geometry optimization and energy calculations, a lattice constant of 0.3577 nm is determined through optimizing the diamond crystalline structure. This value is similar to the experimental value of 0.3567 nm [35]. To ensure the reliability of our results, H abstraction values on the (0 0 1) and (1 1 1) surfaces in the present study are calculated, as 6.06 eV and 5.85 eV, respectively, in agreement with previously reported theoretical values of 6.10 eV [36] and 4.90 eV [37], respectively. The binding energy of an H atom to a P dopant in the P-doped diamond surface is calculated using Eq. (1):
Fig. 4. Binding energy of P–H as a function of P-doped carbon layer in diamond (0 0 1) and (1 1 1) surfaces. (The P-doped positions are illustrated in Fig. 1.)
ΔEb = EP − H − EP − EH package CASTEP [30], which is based on DFT. A plane-wave basis is set and periodic boundary conditions are used to determine the Kohn–Sham ground state. In specific calculations, a spin-polarized general gradient approximation and the PW91 functional (Perdew-Wang) [31] for exchange correlation energy are used. The Brillouin zone is sampled with the Monkhorst–Pack k-points grid [32] in reciprocal space during self-consistent calculations to identify the electronic ground state. The detailed calculation parameters of slab models of both the diamond (0 0 1) and (1 1 1) surfaces are listed in Table 1; the cut-off energy is set to 280 eV. The choice of k-points set and cut-off energy parameters are selected on the basis of careful test calculations; higher values of these two parameters show an energy difference of only 1.2% in calculations of the H binding energy (Eq. (1)). Fig. 1 presents slab models of both diamond (0 0 1) and (1 1 1) surfaces. The Roman numerals II, III, IV, and V denote P dopant in the second, third, fourth, and fifth C layers, respectively, and the letters A and B denote the positions of P in each C layer. The periodic boundary conditions are used in the calculations. A large vacuum space (> 10 Å [33]) between the slabs (in the z-direction) is used to eliminate interslab interactions. Nine and ten C layers are sufficient to determine the H binding energy with sufficient accuracy for the (0 0 1) and (1 1 1) surfaces, respectively. A further increase in the number of C layers does not render any visible change in numerical value for the H binding energy by less than 0.9%. The various substitutional positions for P are also showed in Fig. 1. Substitutional P dopants in the second, third, fourth, and fifth C layers are investigated in this work. For the (0 0 1) surface, there are one substitutional P position in the second and fifth C layer and two positions in the third and fourth C layer. Because of the high symmetry of the (1 1 1) surface, only one substitutional P position in each C layer is investigated. According to the definition of the P–H complex [22], a P atom is bonded to four C atoms and one H atom. When P dopant is
(1)
where EP–H is the total energy of the diamond surface with a P–H complex, EP is the total energy of the P-doped diamond surface without H, and EH is the energy of the H atom. For the P dopant in the second C layer, the energy barrier of H absorption reaction is estimated by the method in Ref. [24]. The H atom is approached in small steps toward the P dopant in the second C layer, as simulated in Fig. 2. The introduced H atom is frozen in varying sites along the reaction path and finally bonded to P atom, and the rest of the structure is relaxed. The energy barrier can be estimated from the energy profile, which is obtained by the energy of each step as an H atom approaches. For P doped in the third, fourth, or fifth C layer, the migration barrier and reaction path of H atoms from on-surface to the P dopant are calculated using the LST/QST method [29]. 3. Results and discussions It is very difficult to experimentally observe the P–H complex structure and its formation process in diamond surface. Theoretical DFT calculations are therefore very useful. In the present study, the P dopants are substitutionally positioned into C layers II, III, IV, and V, and then the stable P–H complex structures and binding energy are calculated. The formation process of the P–H complex can be considered as the process of H migrating from on-surface to subsurface and finally binding with P dopant in each C layer. 3.1. P–H complex structure and binding energy To obtain P–H complex structures in the diamond surface, the H atom is initially placed at different sites around the P dopant, and then the P–H complex structures and corresponding H sites are obtained after geometry optimization. Schematics of P–H complex structures are 311
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Fig. 5. Schematics of stable positions of H on the diamond (a) (0 0 1) and (b) (1 1 1) surfaces.
there are correspondingly two P–H complex structures for each P position. The P–H complex has a lower energy when H is at the AB1 site than when H is at the AB2 site. This result implies that the P–H complex is most stable when H is at the AB1 site. The P–H complex structures with H atoms at AB1 sites are the main focus here; the calculated structural data, bond populations, and atomic charges of these P–H complexes are summarized in Table 2. The P-C bond length d4 is slightly elongated by the incorporation of H, and it is largest among d1, d2, d3, and d4, which is the same as trend for the bond lengths of the P–H complex structures in bulk diamond [22]. The charges of the P and H atoms in the P–H complex are positive and negative, respectively, which can be explained by the higher Pauling electronegativity of H (electronegativity 2.20) compared with that of P (electronegativity 2.19) [3]. The binding energies of P–H as a function of the P-doped C layer number of the P position, are calculated; the results are shown in Fig. 4. A negative binding energy value means that the binding of H to P is exothermic. The P–H binding energy value is lowest for a P dopant at the II-A site. Thus, H binding to a P dopant in the second C layer is energetically most favorable, which implies that the P–H complex is most stable for P doped into the second layer. The binding energy should mainly include two contributions: (i) the energy of the
shown in Fig. 3. The H of P–H complex has three different sites: antibonded (AB), bond-center (BC) and cross-line (CL) sites. C1, C2, C3, and C4 are C atoms near the P atom, and d1, d2, d3, and d4 represent the bond length between the C atom and P atom. α1 is the bond angle between the P–H bond and the d4 bond. The BC site is between the C and P atom, the AB site is opposite the C4 atom along the d4 axis, and the CL site is near the intersecting line between the two planes (one plane consists of C1, C2, and P sites, the other plane consists of C3, C4, and P sites). We find that the P–H complex structures and corresponding H sites in the diamond surface model are slightly different but similar to those in bulk diamond; specifically, the AB, BC, and CL sites in diamond surface are similar to the antibonding, bond center, and 0 0 1 sites in bulk diamond [38], respectively. For example, for the AB site of H around P within the second C layer in the diamond (0 0 1) surface, α1 is 178.5°, whereas α1 is 180° in bulk diamond. Our energy calculations reveal that H at the AB site has the lowest energy among H atoms at the three sites for P–H complex in each of the four C layers. This result is consistent with the previously reported conclusion that the P–H complex has the most stable structure when H is at anti-bonded site in bulk diamond [38]. Two stable AB sites of H around each P position (these two sites are labeled as AB1 and AB2 sites) are found by energy calculation, and 312
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fixed site and the P dopant in the (0 0 1) surface. The bond population value between these two atoms is positive (0.07), indicating an electron orbital overlap. This value strongly supports our hypothesis that no stable H site exists above the P dopant in the second C layer and that the barrier energy value for the binding of H to P dopant in the second C layer within the diamond (0 0 1) surface is zero. Further calculations reveal that the energy barrier value of H migrating to a P dopant is zero within the (1 1 1) surface. Therefore, P–H complex is easy to form, when the P dopant is in the second C layer within the (0 0 1) or (1 1 1) surface. The energy profiles for the H migration path from on-surface to a P dopant below the second C layer in diamond (a–e) (0 0 1) and (f–h) (1 1 1) surfaces are displayed in Fig. 7. The relaxed surface models in Fig. 7 are the local structures containing the P dopant. The labels below the local structures contain the information related to the P and H sites. For example, (0 0 1)-III-A-AB1 represents a P dopant at position A of the third C layer with H at the AB1 site in the (0 0 1) surface. The P-doped diamond surfaces with H at the surface stable site are chosen as the initial states, and the obtained P-doped diamond surfaces with H at the AB1 site (listed in Table 2) are chosen as the final states for our migration calculations. The (0 0 1)-IV-B-AB2 site is a local energy minimum site between the (0 0 1)-IV-B-S2 and (0 0 1)-IV-B-AB1 sites in Fig. 7(d). The (1 1 1)-III-A-CL1 site is a local energy minimum site between the (1 1 1)-III-A-S1 and (1 1 1)-III-A-AB1 sites in Fig. 7(f), and CL1 refers to a CL site of H around P. The (1 1 1)-IV-A-AB2 site is a local energy minimum site between the (1 1 1)-IV-A-S1 and (1 1 1)-IV-A-AB1 sites Fig. 7(g). The (1 1 1)-V-A-CL1 site is a local minimum site between the (1 1 1)-V-A-S1 and (1 1 1)-V-A-AB1 sites in Fig. 7(h). For the diamond (0 0 1) or (1 1 1) surface, the reaction energy value is positive for H migration from on-surface to a P dopant below the second C layer and its energy barrier value is greater than 0.95 eV–7.09 eV, which implies that formation of the P–H complex is difficult for P dopants below the second C layer. Comparatively, the corresponding reverse reaction energy value is negative for the H migration from a P dopant below the second C layer to on-surface and its energy barrier is relatively lower, which implies that the H atom of the P–H complex is more likely to migrate from the AB1 site below the second C layer to on-surface than from on-surface to a P dopant below the second C layer. Reaction energy values for the migration of H to a P dopant below the second C layer are positive (endothermic reaction), which is inconsistent with the negative binding energy values of P–H (exothermic reaction). This can be explained by that the P–H binding energy consists of energy of H absorption onto the surface and the energy of the H migration reaction, and the energy of H absorption onto the surface is obviously negative. For the diamond (0 0 1) surface, the energy barrier value (0.95 eV) is the lowest for the path (0 0 1)-III-B-S2 to (0 0 1)-III-B-AB1 and is largest (5.58 eV) for the path (0 0 1)-IV-A-S1 to (0 0 1)-IV-A-AB1. This result is consistent with the binding energy being largest for a P dopant at the (0 0 1)-IV-A site. For the diamond (1 1 1) surface, the energy barrier value is lowest (6.43 eV) for the path (1 1 1)-IV-A-S1 to (1 1 1)IV-A-AB1 and largest (7.09 eV) for the path (1 1 1)-V-A-S1 to (1 1 1)-VA-AB1. The energy barrier value for H migrating from on-surface to a P dopant below the second C layer is at least 0.85 eV larger for each Pdoped layer in the diamond (1 1 1) surface than for each P-doped layer in the (0 0 1) surface. This result indicates that the P–H complex is less likely to form for the diamond (1 1 1) surface than for the (0 0 1) surface when a P dopant is in the third, fourth, or fifth C layer during the diamond film growth. Our calculations predict that the energy barrier for H migration from on-surface to subsurface is greater than 4.5 eV ((0 0 1) surface) or 7 eV ((1 1 1) surface) for a P dopant below the fifth C layer. Thus, H migration is difficult. Cases where a P dopant is below the fifth C layer are therefore excluded in the present study.
Fig. 6. The electron density difference map showing the interaction between the fixed H atom and the P dopant. (Blue indicates where charge is lost, red indicates where charge is accumulated, and yellow indicates where charge doesn’t change. The colored atoms are defined in Fig. 1.)
interaction between an H atom and a P dopant in the diamond surface and (ii) the deformation energy of the P-doped diamond surface. A greater interaction between the H atom and P dopant in the diamond surface or less deformation of the P-doped diamond surface, results in lower binding energy. As shown in Table 2, for both the (0 0 1) and (1 1 1) surfaces, the P–H bond populations for P dopants in the third, fourth, and fifth C layers are larger than those for P dopants in the second C layer, which indicates that P dopant and H atom interact more strongly. Therefore, higher H binding energies may be explained by H binding leading to relatively larger geometric deformation for P dopants below the second C layer than for P dopants in the second C layer.
3.2. Energy profiles of H migration The gas chamber contains a large amount of H atoms, and the H atoms above the surface are the main source of H for forming P–H complexes in the subsurface. The stable P–H complex for each P position in (0 0 1) and (1 1 1) surface are obtained in the previous section. In this section, we calculate the energy profiles of H migrating from onsurface to P dopants to investigate the formation process of P–H complexes. For P dopant in third, fourth, or fifth C layer, there are two stable sites of H above the P dopant on diamond (0 0 1) surface, and one on (1 1 1) surface, as shown in Fig. 5. For P at the (0 0 1)-III-A or (1 1 1)-IIIA position, the S1 site of H is a highly symmetric position. For P at the (0 0 1)-III-B, the S2 site of H is a highly symmetric position. For P at the (0 0 1)-IV-A, (0 0 1)-V-A, (1 1 1)-IV-A, or (0 0 1)-V-A position, the stable site for H on the surface is not exactly at but near a highly symmetric position; the specific stable positions of H are determined through geometry optimization calculations. Numerous other stable sites for H exist on the surface but are excluded in this work because H migration barriers from these sites to P dopant sites in the subsurface are higher than those from the stable sites in Fig. 5 to P dopant sites in the subsurface. For P dopant in the second C layer within the diamond (0 0 1) surface, no stable site of H exists above the P dopant and the energy barrier value for H migrating to the P dopant is zero. We calculated the stable site for H on the pure diamond (0 0 1) surface, and then substituted a P dopant for a C atom in the second C layer while leaving the H atom at the stable site fixed during relaxation. The H electron density difference map in Fig. 6 shows a strong interaction between the H at the 313
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Fig. 7. Energy profiles for H migration from the on-surface to the subsurface in diamond (a–e) (0 0 1) and (f–h) (1 1 1) surface. (Energy unit: eV. The colored atoms are defined in Fig. 1.)
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Fig. 7. (continued)
implies that fewer P donors could be passivated and more P atoms could act as donors in the (1 1 1) surface than in the (0 0 1) surface, consistent with the experimental finding of a lower P donor fraction in the (0 0 1) surface than in the (1 1 1) surface [13–15]. Some researchers have speculated that the (0 0 1) surface is preferred for future applications, because the room temperature Hall mobility of the diamond (0 0 1) surface is four times greater than that of the diamond (1 1 1) surface [12,15]. However, our results suggest that P-doped diamond should be fabricated on the (1 1 1) surface because the P–H complex is less likely to form for a P dopant below the second C layer in (1 1 1) surface than for a P dopant below the second C layer in the (0 0 1) surface.
3.3. Discussions The formation of P–H complex is one of the reasons for compensation of carriers in diamond film [16–18]. Thus, the P–H complexes should be eliminated during the diamond film growth, to obtain a highquality P-doped diamond film. Among the four P-doped C layers, a P–H complex is most likely to form when P dopant is in the second C layer. During the growth of a diamond film, if P–H complexes are not eliminated, a large amount of P–H complexes in the second carbon layer will be brought into bulk diamond. Our results suggest that H atoms should be prevented from binding to P when P dopant is present in the second C layer. When a P–H complex forms in the third, fourth, or fifth carbon layer, H migration from the subsurface to on-surface is an exothermic reaction. Therefore, the P–H complex could be removed by imposing an external energy field (such as an increase in temperature) to increase the tunneling probability of H migration to on-surface when a P–H complex is in the third, fourth, or fifth C layer. When a P dopant is in the third, fourth, or fifth C layer during the diamond film growth, a P–H complex is less likely to form in the diamond (1 1 1) surface than in the (0 0 1) surface. This result further
4. Conclusions H-terminated (0 0 1) and (1 1 1) diamond models are built to mimic the as-grown CVD diamond surface. H binding to a P dopant in diamond (0 0 1) and (1 1 1) surfaces is systematically calculated by DFT. The following conclusions are drawn from the results: (1) P–H complex structures for each P dopant positions in diamond surfaces are obtained. For each P dopant, the most stable P–H 315
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References
complex forms when H occupies the AB1 site around the P dopant. There are AB, BC, and CL sites of H around P dopant in P–H complex structure, and the P–H complex has the lowest energy when H occupies the AB site among these three sites. Moreover, for each P position, there are two AB sites (AB1 and AB2 sites) of H. The P–H complex has a lower energy when H occupies the AB1 site rather than the AB2 site, which implies that P–H complex is most stable when H occupies the AB1 site. (2) The stability of P–H complexes for each P-doped position in diamond (0 0 1) and (1 1 1) surfaces is compared. For P doped in the second C layer, the P–H binding energy values are −4.61 eV and −4.44 eV in the (0 0 1) and (1 1 1) surfaces, respectively, which are the lowest among the four P-doped C layers. This implies that the P–H complex is more energetically stable when P is doped within the second C layer than when P is doped in other C layers. (3) The H migration process and formation mechanism of P–H complexes in diamond surfaces are clarified. For P doped in the second C layer, H migration from on-surface to the P dopant is an exothermic process and its energy barrier is zero. For P doped below the second C layer, H migration from on-surface to the P dopant is an endothermic reaction and its energy barrier is greater than 0.95–7.09 eV. This finding indicates that a P–H complex is more likely to form when P is doped within the second C layer than when P is doped below the second C layer. Comparatively, the corresponding reverse reaction is exothermic for the H migration from the P dopant below the second layer to on-surface. This result implies that an H atom of the P–H complex is more likely to migrate from the AB1 site below the second C layer to on-surface than from on-surface to a P dopant below the second C layer. (4) P–H complex is more likely to form for the diamond (0 0 1) surface than for the diamond (1 1 1) surface when the P dopant is in the third, fourth, or fifth C layer during the growth of a diamond film. The H migration energy barrier from on-surface to a P dopant below the second C layer is at least 0.85 eV greater for each of the P-doped C layers in the diamond (1 1 1) surface than for each of the P-doped layers in the diamond (0 0 1) surface. It also indicates that fewer P donors could be passivated in the (0 0 1) surface than in the (1 1 1) surface.
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The research presented here provides detailed information about the structures and formation process of P–H complexes during diamond film growth. Furthermore, it provides guidance on how to eliminate P–H complex formation for fabricating a high-quality P-doped diamond film. Specifically, (i) to avoid the formation of P–H complexes from the outset, H atoms should be prevented from binding with P dopant in the second C layer. (ii) Ideally, P–H complexes could be removed by imposing an external energy field (such as an increase in temperature) to promote H migrating from subsurface to on-surface when the P dopant is in the third, fourth, or fifth C layer. (iii) P-doped diamond should be fabricated on the (1 1 1) surface, because the P–H complex is less likely to form for P dopant atoms below the second C layer in the (1 1 1) surface than for P dopant atoms below the second C layer in the (0 0 1) surface.
Acknowledgements This work is supported by the International Cooperation Research Project of Shenzhen (GJHZ20180413182004161) and the National Natural Science Foundation of China (51727901).
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2018.12.018. 316
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