The Influence of B, N and Si Doping on the CH₃ Adsorption on the Diamond Surface Based on DFT Calculations

Abstract

To better understand the influence mechanism of boron, nitrogen and silicon dopants on the growth of chemical vapor deposition (CVD) diamond film, density functional calculations have been performed to reveal the different impact of the impurities on the CH₃ adsorption on diamond surface. The substituted doping and radical doping of diamond (111) and (100) − 2 × 1 surface are both considered. The calculation results indicate that the CH₃ radicals are hardly adsorbed on nitrogen atoms and thus may cause vacancy in the diamond lattice easily. Boron substituted doping will disfavor the adsorption of CH₃ due to the lacking of valence electron. However, the empty p orbitals of boron atom will help the chemical adsorbing of CH₃ radicals. The substituted silicon doping has little influence on the CH₃ adsorption, as Si atom has the same outer valence electron structure with C atom. In the case of radical doping, the adsorption energy of CH₃ will be reduced due to the steric hindrance between NH₂ or SiH₃ with CH_3. The adsorption energy can be slightly enhanced when BH₂ radical is pre-adsorbed on diamond (111) surface. However, the BH₂ pre-adsorbed on diamond (100) − 2 × 1 surface may interact with surface radical carbon site and result in a large reduction of CH₃ adsorption energy. Thus, the boron doping may hinder the formation of the (100) facet during the CVD diamond deposition under a certain condition.

1. Introduction

Chemical vapor deposition (CVD) diamond films have been wildly used in electronic, mechanical, optical, and various other fields due to their unique properties. Furthermore, CVD is a suitable method to change the properties of diamond films easily [1,2,3,4,5]. Doping the diamond with boron, silicon, nitrogen, phosphorus, lithium or europium allows the semiconductor [6] to form luminescent centers [3,7] or a nitrogen-vacancy (NV) center [8,9]. Additionally, experimental investigations reported that the introduction of impurities into the plasma can also affect the growth rate [10], surface morphology, quality, tribological properties or mechanical properties of diamond film [11,12,13,14,15,16,17,18,19]. However, the influence mechanism beneath the experimental phenomenon is not clear yet. How to explain these experimental results from the point view of growth theory is of great significance to choose different dopants to get the desired diamond properties we want.

The surface chemistry of diamond films prepared by CVD is very complicated, it includes different steps such as adsorption, H abstraction and surface migration of the radicals. The growth theory of diamond films are intensively studied based on the molecular orbital theory, density functional theory (DFT), Quantum Mechanical or Monte Carlo method [20,21]. It was found that the CH₃ adsorption is one of the main growth steps of the diamond deposited, using the hot filament chemical vapor deposition (HFCVD) method under the H₂ and CH₄ atmosphere [22,23]. DFT calculation allows the better understanding of the influence of the impurities on the growth of diamond [24,25,26,27,28,29,30,31]. However, it still need systematically comparing of the impacts of different doping on the growth of CVD diamond films.

In this study, density functional theory has been used to investigate the influence of doping sources on the growth mechanism of CVD diamond films at atomic scale. Specifically, the influence of three doping sources (B, N and Si) on the CH₃ adsorption on diamond (111) and (100) − 2 × 1 surface are studied. Firstly, the CH₃ radical adsorption on the substituted atom is compared to find out whether the dopants will affect the diamond structure. The influence of doped radicals on the adsorption of CH₃ is also studied to reveal the impacts of dopants on the epitaxial growth of diamond. It provides an effective theoretical basis for the understanding of the experimental results.

2. Methodology

All theory calculations are carried out using Cambridge Sequential Total Energy Package (CASTEP) code, which is based on density functional theory [32]. The PW91 functional and spin-polarized general gradient approximation are selected under the periodic boundary conditions. The number of k points (2 × 2 × 1) was generated using the Monkhorst-Pack scheme, and the cutoff energy was set to 280 eV [18,33]. The final morphology of diamond films is determined by the growth rate of diamond (111) and (100) facets. Thus, diamond (111) and (100) models are both used to study the adsorption energy in this study. Although it is reported that the substitutional B and N dopants within the second C layer will have the largest influence on the diamond growth rate especially on the rate-determining H-abstraction step [34]. As the aim of this study is to explore whether the CH₃ radicals can still be adsorbed on the dopants, the center carbon atom in the first C layer is substituted by boron, nitrogen or silicon atoms. The calculating model shown in Figure 1 indicates a substituted boron doped diamond slab. The pink, gray and white balls are boron, carbon and hydrogen atoms, respectively. The H-terminated diamond (111) and (100) − 2 × 1 slab is composed by 4- and 6-layers carbon atoms, respectively. The thickness of the vacuum is set as 10 Å to avoid the interfering between the slabs. Two layers of carbon atoms of diamond (111) and three layers of diamond (100) − 2 × 1 in the bottom are fixed, while the other atoms can relax freely.

When the effects of doped radicals on the adsorption energy of CH₃ are studied, the calculation mode is built, as shown in Figure 2. The CH₃ radical is adsorbed on the active carbon site at the center of the model, the NH₂, BH₂ or SiH₃ doped radicals are adsorbed at the C atom adjacent to the active carbon site according to the doping conditions. Due to the high symmetry of the diamond (111) surface, the carbon site adjacent the center carbon site is all equivalent. However, there are three different adsorption sites for the doped radicals on the diamond (100) − 2 × 1 reconstructed surface as shown in Figure 2b.

3. Results and Discussions

3.1. The Adsorption of CH₃ on Different Doped Atoms

The adsorption energy is defined as:

$$\mathsf{\Delta }{E}_{adsorb}=E_{D\text{-}rad}-E_D-E_{rad}$$

(1)

Where $\mathsf{\Delta }{E}_{adsorb}$ is the adsorption energy, $E_D$ and $E_{D\text{-}rad}$ are defined as the energy before and after the adsorption of radical, respectively. $E_{rad}$ is the energy of radical in gas phases.

The adsorption energy of CH₃ on undoped and doped (111) and (100) − 2 × 1 diamond surface is listed in

Table 1. The adsorption energy of CH₃ on undoped and substituted doped diamond surface.

$\mathbf{\Delta }{\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}\mathit{o}\mathit{r}\mathit{b}}(\mathbf{kJ}/\mathbf{mol})$	(111)	(100)
C	−312.82	−349.40
B	−130.45	−234.33
Si	−360.90	−333.94
N	0.07	−37.44

. C, B, Si, N correspond to the case of undoped diamond, boron doped, silicon doped and nitrogen doped diamond, respectively. It is well known from the solid-state theory, that when the adsorption process is exoenergetic, the adsorption energy is negative and the radical can be adsorbed on the surface. Moreover, the more negative of the energy, the more stable of the adsorption. Otherwise, the radical cannot be adsorbed on the surface.

Generally, the adsorption energy of CH₃ on substituted doped diamond surface is lower than that on undoped diamond surface. The adsorption energy is especially low in the case of nitrogen doped diamond. The value is almost 0 in the case of nitrogen doped diamond (111) surface. It shows that the CH₃ radical can hardly adsorbed on N atom. Moreover, the CH₃ adsorption energy is only −37.44 kJ/mol when adsorbed on the nitrogen doped diamond (100) surface. The reason for the low energy may arise from the covalent bond weakening caused by the extra electron in N. The results reveal that N atoms disfavor the epitaxial growth of diamond on the doped site. Thus, there will be a vacancy near the N atoms and induce a larger lattice defect. Since Si has the same outer electronic structure as C, the adsorption energy of CH₃ on silicon doped diamond surface is close to that on undoped diamond surface.

Due to the adsorption energy of CH₃ on different doped diamond (100) and (111) surface sharing a same variation tendency, the cases of CH₃ adsorbed on diamond (111) surface is used for further analysis. Since the atoms in the surface region can move freely in the calculation, the change of the model geometry and the electronic structure before and after adsorption will have a significant impact on the final adsorption energy. Firstly, the charge distribution of diamond surface before CH₃ adsorption as shown in Figure 3 is analyzed. The total charge density distribution range in 0~2.35. It can be seen that the total electron density of boron doped, silicon doped and nitrogen doped diamond is similar with that of undoped one. The results indicated that the bonding structure between doped atoms and carbon atoms is similar, and there is no chemical bond breaking. It is well known that there are five valence electrons in the outer layer of N atom; pair electrons will form when the N atom interacts with three carbon atoms in the secondary layer of the diamond slab. The forming of pair electrons will enable a stable electronic structure of the diamond surface. Therefore, it can be seen from the total electron density of the diamond surface that the surrounding region of N atom is a charge enrichment region. Moreover, the charge density difference is also analyzed, and the charge density range is −0.7~0.7. The region where the electronic decreased is shown in blue, electronic enrichment is shown in red, and white indicates that electron density is almost not changed in one region. As indicated in Figure 3b, the boron atom center is blue while the nitrogen atom center is red. The results reveal that boron atom loses electrons while the nitrogen atom gets electrons. The results of Mulliken population analysis show that C has no electron gain or loss, Si lost 1.27 electrons, B loses 0.62 electrons, and N gets 0.39 electrons.

For all kinds of doping, the electron density difference is viewed at a selected plane with the same height. However, the bond length of Si-C is larger than that of the original C-C after silicon doping, so the plane may closer to the center of the Si-C bond compared with C-C, B-C and N-C bond. Consequently, the electron density difference shows a more pronounced electronic enrichment in the case of silicon doped diamond surface.

Figure 4 illustrates the local density of the state of the substituted atom after the adsorption of CH₃. It should be mentioned that the total energies at the zero-energy point for different models may not be identical. It can be seen that the 2s and 2p orbitals of the carbon atom have overlapped within the region of −20~−7.5 eV, and the overlap of 2s and 2p valence electron orbitals of B atom occurs in the energy region of −15~−2.5 eV. Furthermore, the overlap of 2s and 2p orbitals of silicon atom occurs in the regions of −10~−2.5 and −15~−12.5 eV. However, the overlap for the N atom within the entire energy region is very small. The results indicate that C, B, and Si atoms may bond with CH₃ due to the overlapping of the orbitals. However, N atom directly obtained three electrons provided by the C atoms bonded with the N atom located in the sublayer of the diamond bulk. As a result, the N atom comes to a full electron state before CH₃ adsorbed on the N atom. Consequently, the bonding strength between N and CH₃ is weak. The adsorption of CH₃ on the substituted nitrogen atom may be a reversible adsorption and a vacancy may easily form near the nitrogen atom.

The bond population between the C atom of adsorbed CH₃ and surface substitutional doped atom are calculated as follows: C-C, 0.75; C-B, 0.81; C-Si, 0.72; C-N, 0.43. The C-N bond presents a significantly lower population value compared with other types of bonds. The results indicate C-N bond is relative weaker [35]. C-Si bond shows a similar bond population value with C-C bond due to Si and C atom having the same outer valence electron structure. It also shows that the adsorption energy of CH₃ on the Si doped diamond surface is lower than that on the undoped diamond surface. The population value of B-C is the largest, thus the B-C bond is strongest among all cases. The results indicate that the B atoms can be easily incorporated into the diamond lattice and will not have a greater impact on the further growth of the diamond.

Although the adsorption energy of CH₃ on the substituted N atom within the (100) diamond surface is lower than that of other doping cases, it still has a certain adsorption energy compared with the almost 0 in the nitrogen doped (111) diamond surface. Figure 5 shows the structure of the nitrogen doped (100) diamond before and after the adsorption of CH₃ on the substitutional nitrogen atom. It can be found that the distance between N and C3 atom increases to 2.438 Å after the CH₃ adsorption, and the N-C3 bond breaks, which indicate the occurring of the so-called beta scission rearrangement [35]. N atom only bonds with Cs1 and Cs2 atom in the secondary C layer, and N-Cs1 and N-Cs2 bond are symmetrical distributed with an equal bond length of 1.48 Å. Therefore, it has a certain adsorption energy when CH₃ adsorbed on the nitrogen doped (100) diamond surface.

3.2. The Effects of Doped Radicals on the Adsorption of CH₃

The interaction between the doped radicals and CH₃ adsorbed on the surface may change the structural stability. The stable of the surface structure before the adsorption will reduce the adsorption energy, while the stable of the structure after adsorption will increase the adsorption energy.

Table 2. CH₃ adsorption energies in the presence of different adsorbed dopants radicals.

$\mathbf{\Delta }{\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}\mathit{o}\mathit{r}\mathit{b}}(\mathbf{kJ}/\mathbf{mol})$	(111)	(100)
		1	2	3
BH2	−320.94	−363.34	−345.23	−264.33
SiH3	−271.25	−346.77	−297.71	−297.11
NH2	−283.65	−319.14	−317.38	−346.77
CH3	−267.87	−289.54	−299.67	−327.63
H	−314.69		−349.40

shows the CH₃ adsorption energies in the presence of different adsorbed dopants initially adsorbed on the carbon atoms near the CH₃ adsorption site. For comparison, the adsorption energy of CH₃ is calculated under the same conditions when the adsorbed dopants are replaced by H or CH₃. The former case represents the undoped diamond growth. While the latter is mainly calculated to describe the difference of electronegativity between C, B, N, and Si, which in turn may lead to electron delocalization in the surface region of the diamond lattice. Generally speaking, doped radicals or CH₃ radicals will reduce the CH₃ adsorption energy compared with the undoped cases. It means that pre-adsorbed doped radicals may result in a transfer of this elementary reaction into a rate-limiting step, and thus hinder the epitaxial growth of diamond on (111) and (100) surface [33]. SiH₃ has a great influence on the adsorption energy of CH₃. It will reduce 35–52 kJ/mol of the CH₃ adsorption energy except in the case that SiH₃ is located at the adsorption site 1 of diamond (100) surface.

However, the BH₂ radical seems have a different impact on the CH₃ adsorption. When BH₂ is adsorbed on the site 1 of diamond (100) surface, the adsorption energy slightly increases about 14 kJ/mol compared with that of undoped case. Moreover, CH₃ adsorption energy of CH₃ when BH₂ is adsorbed on the diamond (111) surface is higher than that on undoped diamond (111) surface. However, it is smaller than that of adsorption site 1 cases of diamond (100) surface, the adsorption energy increases about 6 kJ/mol. The result indicates that the BH₂ may beneficial to the CH₃ adsorption in these two cases. The adsorption of BH₂ at site 2 has a little impact on the adsorption energy which decreases only about 4 kJ/mol. Surprisingly, when BH₂ is at the adsorption site 3, the adsorption energy will decrease significantly, the value is as high as 85 kJ/mol.

T. Van Regemorter et al. pointed out that NH₂ will have steric hindrance effect with CH₃ [33]. Similarly, there is a strong steric hindrance between SiH₃ and CH₃. The steric hindrance will bring about the unstable surface structure after CH₃ adsorption, thus the adsorption energy is greatly reduced when NH₂ or SiH₃ is pre-adsorbed on diamond surface. Compared with NH₂ and SiH₃, BH₂ has a completely different effect on CH₃ adsorption. For diamond (111) and diamond (100) surface, when BH₂ is adsorbed on adjacent C atoms, the final structure of CH₃ adsorbed on diamond (111) and diamond (100) does not show obvious steric hindrance between CH₃ and BH₂. This is because BH₂ has an empty 2p orbit rather than non-bonding valence electron pairs existed in NH₂, which reduces the steric hindrance effect.

The optimization geometric structure of diamond when BH₂ is adsorbed on diamond (100) surface is shown in Figure 6. The results indicate that BH₂ will interact with active C site (C*) before the CH₃ adsorption when BH₂ is at the adsorption site 3 of diamond (100) surface. Consequently, the B atom and C* will form a new bond. The bonds between the B atom and the two adjacent carbon atoms are symmetrical and their bond length are about 1.6 Å. As a result, before the CH₃ adsorption, the diamond surface comes to a relatively stable energy when BH₂ is adsorbed at site 3. Consequently, the CH₃ adsorption energy will be reduced. Although there are no bonds between the B and C* atoms in the site 1 and site 2 cases, BH₂ radical has an approaching tendency to C*. Therefore, the adsorption energy of CH₃ will not be reduced when BH₂ is adsorbed on the site 1 and site 2. On the contrary, it may slight enhanced due to the absent of spatial exclusion between BH₂ and CH₃.

4. Conclusions

Hydrogen terminated diamond (111) and (100) − 2 × 1 models are first used to study the adsorption possibility of CH₃ radical on substituted doped atoms. The results show that substituted silicon doping have little influence on the CH₃ adsorption due to the same outer valence electron structure between Si and C atom. The CH₃ radicals have a low adsorption energy on nitrogen doped diamond surface because of the fullness of outer electrons of nitrogen atom before the CH₃ adsorption. The adsorption of CH₃ on nitrogen doped diamond surface is only physical adsorption. While in the case of boron doped diamond, the substituted boron atom will form covalent bonds with the three-carbon atom of secondary layer of the diamond lattice. As a result, boron atoms have no redundant valence electrons, the CH₃ adsorption energy is greatly reduced. However, due to the existence of empty p orbitals of boron atoms, boron doped diamond still has a certain bonding ability. Thus, the adsorption of CH₃ on the substituted boron doped diamond surface is still chemical adsorption. Generally speaking, the adsorption energy of CH₃ on the impurity atoms is decreased, which indicates that structural defects are likely to occur near substituted doped atoms.

Subsequently, the impacts of doped radicals on the CH₃ adsorption during the initial growth of diamond films is also investigated. The results show that NH₂ or SiH₃ have a steric repulsion with CH₃, resulting in a decrease of the CH₃ adsorption energy. SiH₃ radicals will reduce the CH₃ adsorption energy by 35~52 kJ/mol. The adsorption energy of CH₃ is less affected when NH₂ is adsorbed on the adsorption site 3 (see Figure 6) of diamond (100) − 2 × 1 surface. Besides that case, the presence of NH₂ on the diamond (111) and (100) surfaces will reduce the adsorption energy of CH₃ by about 30 kJ/mol. The adsorption of BH₂ radicals on the diamond (100) − 2 × 1 adsorption site 3 will interact with the surface radical carbon site, resulting in a stable structure before the CH₃ adsorption. Consequently, the CH₃ adsorption energy is largely decreased by about 85 kJ/mol. However, the empty p orbital in the boron atom of BH₂ radical relieves the steric hindrance between BH₂ and CH₃ radicals. Therefore, the other BH₂ adsorption cases show little influence on the adsorption of CH₃.

The comparison of the influence of dopants on the CH₃ adsorption indicates that the Si and B atoms will not have a greater impact on the further growth of the diamond. However, the boron doping may reduce the growth rate of the diamond (100) facet at a certain CVD diamond deposition parameter. While lower the adsorption energy of CH₃ on nitrogen atom may hinder the growth of diamond near the doping point and form a vacancy diamond structure easily.