⇦Chinese Physics Letters, 2019, Vol. 36, No. 11, Article code 116101 Comparative Study of Substitutional N and Substitutional P in Diamond * Hong-Yu Yu (于洪雨)1,2, Nan Gao (高楠)1**, Hong-Dong Li (李红东)1, Xu-Ri Huang (黄旭日)2, Tian Cui (崔田)1 Affiliations 1State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012 2Institute of Theoretical Chemistry, Jilin University, Changchun 130012 Received 14 June 2019, online 21 October 2019 *Supported by the National Natural Science Foundation of China under Grant Nos 11704143, 11604023, 51672102, 51972135, 51632002, 51572108, 91745203 and 11634004, and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No IRT_15R23.
**Corresponding author. Email: gaon@jlu.edu.cn Citation Text: Yu H Y, Gao N, Li H D, Huang X R and Cui T et al 2019 Chin. Phys. Lett. 36 116101    Abstract Based on density functional theory calculations, it is found that for substitutional N in diamond the $C_{3v}$ symmetry structure is more stable, while $C_{3v}$ and $D_{2d}$ symmetry patterns for the substitutional P in diamond have comparable energies. Moreover, the substitutional N is a deep donor for diamond, while P is a shallow substitutional n-type dopant. This is attributed to the different doping positions of dopant (the N atom is seriously deviated from the substitutional position, while the P atom nearly locates in the substitutional site), which are determined by the atomic radius. DOI:10.1088/0256-307X/36/11/116101 PACS:61.72.-y, 71.20.-b © 2019 Chinese Physics Society Article Text Diamond is one of the most promising semiconductor materials because it has the outstanding characteristics of high thermal conductivity, high dielectric breakdown field, high carrier mobility, corrosion resistance, and so on. Intrinsic diamond is a wide band-gap semiconductor.[1] To enable diamond to be used as a semiconductor with a narrower band gap in electronic devices, it is necessary to dope it with foreign atoms, and therefore both p-type and n-type diamonds are required. At present, p-type semiconductors have been successfully obtained by doping B into diamond (0.37 eV),[2] while there are still significant challenges to achieve shallow n-type donors. In the past few decades, a number of experimental and theoretical approaches have been implemented to realize n-type diamonds. The dopants include alkali metals (Li and Na),[3,4] alkaline-earth metals (Be and Mg),[5] pnictogens (N, P, As and Sb),[6–14] chalcogens (O, S, Se and Te),[15–17] and halogens (F, Cl, Br and I),[18] and so on. N is easily doped as a donor in diamond, and it is one of the most common impurities in natural and N-doped chemical vapor-deposited diamonds, thus the N-doped diamond has been extensively studied.[7,19,20] However, the donor level of N-doped diamond (1.7 eV[21]) is very deep to make the conductivity negligible at room temperature. Luckily, the P-doped diamond has a relatively shallow donor level of 0.57 eV,[22,23] and the dopant concentration was continuously improved in recent years.[24] However, the low electron mobility and conductivity seriously hinder its application as a room temperature semiconductor.[25] Even so, an ultraviolet light-emitting diode based on a diamond p–n junction was successfully realized,[26] and P is considered as the only reliable n-type dopant up to date. Considering that both N and P atoms are the same group V elements, while only the latter is a reliable donor. In this work, the structural models and electronic properties of substitutional N (N$_{\rm sub}$) and substitutional P (P$_{\rm sub}$) in diamond are comparably investigated utilizing the density functional theory (DFT) method. It is found that the N$_{\rm sub}$ (P$_{\rm sub}$) in diamond is a deep (shallow) donor, attributed to the deviated (nearly substitutional) N (P) dopant position determined by the atomic radius. Our calculations were carried out using the DFT technique combined with projector augmented wave potentials[27] implemented in Vienna ab-initio simulation package (VASP) code.[28] The exchange-correlation functions were expressed by the Perdew, Burke, and Ernzerhof (PBE) function within the generalized gradient approximation (GGA),[29] and the cutoff energy of 520 eV was set to enable excellent convergence of the energy differences, stress tensors, and structural parameters. To minimize the finite-size effects, a large supercell containing 512 atoms was used in the ${\it \Gamma}$-point approximation for molecular dynamics (MD) simulation. The MD simulations were implemented in the isobaric isothermal ensemble[30] at 300 K and atmospheric pressure, and the time step of 1.0 fs and total simulation time of at least 10 ps were used. Average lattice constants derived from the MD simulations were optimized with a Monkhorst–Pack scheme set, and then the total energy, band structures, density of states (DOS) were calculated with the same $k$ mesh of $3\times 3\times 3$. The tolerance for a total energy within 0.2 meV/atom, and the inter-atomic force within 0.01 eV/Å were taken in the calculations. To investigate the structural stabilities of N$_{\rm sub}$ and P$_{\rm sub}$ in diamond, the formation energy $E_{\rm F}$ was calculated following the equation[31] $E_{\rm F}(X)=E_{\rm tot}(X)-511\times E_{\rm C-bulk}-\mu_{x}+E_{\rm corr}$, where $E_{\rm tot}(X)$ was the total energy of optimized structure with impurity $X$, $E_{\rm C-bulk}$ was the energy of the bulk diamond per carbon atom, $\mu_{x}$ was the chemical potential of N or P atom, $E_{\rm corr}$ was the correction for periodic boundary conditions, and here it was 0.27 eV for the cubic supercell.[31] First, we calculate the structural parameter and band structure of pristine diamond to verify the reliability for the calculation parameters setting. The lattice parameter of pristine diamond is 3.573 Å (Fig. 1(a)), which agrees well with the experimental value of 3.567 Å.[32] Moreover, the indirect band gap of bulk diamond is 4.10 eV (Fig. 1(b)), which is similar to other calculation results,[33,34] and the difference between our results with the experimental value (5.48 eV[32]) is caused by the underestimation of PBE calculations. Thus the calculation parameters set in this study are reliable.
cpl-36-11-116101-fig1.png
Fig. 1. The structural model (a) and band structure (b) of pristine diamond with the unit cell.
cpl-36-11-116101-fig2.png
Fig. 2. (a) The distances between the N atom and four adjacent C atoms (named as $d_{{\rm NC}_i}$, $i=1$, 2, 3 and 4) as a function of MD steps. (b) The partial structures of N$_{\rm sub}$ before MD calculations with $T_{d}$ symmetry. Here $d_{{\rm NC}_1}=d_{{\rm NC}_2}=d_{{\rm NC}_3}=d_{{\rm NC}_4}=1.61$ Å. (c) The N$_{\rm sub}$ structures after MD calculations with $C_{3v}$ symmetry. Here $d_{{\rm NC}_1}=d_{{\rm NC}_2}=d_{{\rm NC}_3}=1.48$ Å, $d_{{\rm NC}_4}=2.04$ Å, and $\angle {\rm C}_{1}{\rm NC}_{2}=\angle {\rm C}_{2}{\rm NC}_{3}=\angle {\rm C}_{1}{\rm NC}_{3}=114.9^{\circ}$. The brown balls are C atoms, and the blue ball is the N atom.
Since the MD simulations provide the structure parameters changing as a function of time at room temperature, it has been used to predict the structure of substitutional S in diamond.[35] Thus the MD calculations are used here to predict the substitutional models. The center C atom is replaced by an N (or P) atom as the initial structure of MD simulation of N$_{\rm sub}$ (or P$_{\rm sub})$ in diamond. Figure 2(a) shows the distance between N atom and four adjacent C atoms as a function of MD simulation time. One can see that $d_{{\rm NC}_4}$ increases sharply to $\sim $2.0 Å, and the other three $d_{\rm NC}$ decrease to $\sim $1.5 Å at 800 steps, then the simulation achieves equilibrium. The further DFT optimization is performed to obtain a reliable structure based on averaging the lattice parameters after 6000 steps (6.0 ps). As shown in Fig. 2(b), before MD calculations, it has a $T_{d}$ symmetry (named as N$_{T_{d}}$). After MD calculations, the N atom forms a $C_{3v}$ symmetry center with four adjacent C atoms (named as N$_{C_{3v}}$). Through the total energy calculations, the N$_{C_{3v}}$ is more stable with a lower total energy.[9] The calculated $E_{\rm F}$ for N$_{C_{3v}}$ is 4.12 eV, which is close to 3.96 eV in the previous work.[36]
cpl-36-11-116101-fig3.png
Fig. 3. The band structures, total DOS and PDOS of N, C$_{1}$, C$_{2}$, C$_{3}$ and C$_{4}$ atoms, and partial ELF of N$_{\rm sub}$ in diamond [(a), (c), (e)] before MD calculations with $T_{d}$ symmetry, and [(b), (d), (f)] after MD calculations with $C_{3v}$ symmetry. The black and red lines are the spin-up and spin-down band structures, respectively.
The band structures of N$_{\rm sub}$ in diamond with $T_{d}$ and $C_{3v}$ symmetry show that the spin-related donor levels are split (Figs. 3(a) and 3(b)). For the case of N$_{T_{d}}$ (N$_{C_{3v}}$), the occupied spin-up donor level is about 0.2 eV (1.6 eV) lower than the conduction band minimum (CBM). This indicates that N$_{\rm sub}$ in diamond before MD calculations is a shallow donor, while after MD optimizations, it is the deep donor. This is consistent with the previous conclusion that N$_{\rm sub}$ in diamond is not a good donor.[21] Moreover, the donor levels are mainly contributed by the substitutional N atom and adjacent C atoms (Figs. 3(c) and 3(d)). To analyze the different n-type donor levels in N$_{\rm sub}$, we compare the partial electron localization functions (ELFs) of N$_{\rm sub}$ with $T_{d}$ and $C_{3v}$ symmetry (Figs. 3(e) and 3(f)). For N$_{T_{d}}$, the N atom is four-coordinated with the electrons equally distributed among the four N–C bonds. For the case of N$_{C_{3v}}$, the N atom is threefold coordinated, with the remaining two electrons forming a lone-pair orbital, which is directed towards the unpaired electron of the fourth C atom (Fig. 3(f)). The repulsion force appears between the lone-pair electron and the unpaired electron, which is consistent with the larger distance between the N atom and the fourth C atoms. The asymmetrical electron distribution around the dopant leads to the donor level moved down, making N$_{\rm sub}$ in diamond a deep n-type donor.
cpl-36-11-116101-fig4.png
Fig. 4. (a) The band structure of NV center, [(b), (c)] the partial charge distribution for the two donor levels.
Considering that the nitrogen-vacancy (NV) center is generally observed experimentally,[37] and it is considered to be one of the promising candidates for quantum information processing and quantum computing,[38] we substitute two adjacent C atoms with an N atom and a vacancy. The calculated $E_{\rm F}$ is 6.39 eV, being close to the previous result of 6.21 eV.[36] The band structure in Fig. 4(a) shows two donor levels splitting. Moreover, the donor level on the bottom is mainly contributed by the N atom, and the donor level in the upper side is from the three C atoms adjacent the vacancy (Figs. 4(b) and 4(c)). For P$_{\rm sub}$ in diamond, the bond lengths and bond angles of the P atom and its adjacent C atoms are almost equal as time increases (Figs. 5(a) and 5(b)), denoting the slight variation of structural parameters. We refine the structural parameters as a function of MD step, and statistical average the lattice parameters after 5000 steps (5.0 ps). It is found that two structural characteristics of P$_{\rm sub}$ with $C_{3v}$ and $D_{2d}$ symmetries (named as P$_{C_{3v}}$ and P$_{D_{2d}}$ frequently appear, and transform each other. The bond lengths and angles around 5400 and 5600 steps with P$_{C_{3v}}$ and P$_{D_{2d}}$ characteristics are listed as examples in Figs. 5(c) and 5(d), respectively. Through the further DFT optimizations, the P$_{C_{3v}}$ structure has one slightly longer (1.75 Å) and three short (1.70 Å) P–C bonds, and bond angles satisfy the relation of $\angle {\rm C}_{1}{\rm PC}_{2}=\angle {\rm C}_{2}{\rm PC}_{3}=\angle {\rm C}_{1}{\rm PC}_{3}=111.4^\circ$, while the latter has four equal P–C bond lengths (1.71 Å). The difference of structural parameters for the two doped structures is slight (Figs. 5(e) and 5(f)), and the total energy of P$_{C_{3v}}$ in diamond is only 0.01 eV lower than that of P$_{D_{2d}}$, indicating that both structures possibly appear. This is similar to the lowest-energy structures in Ref. [39]. The $E_{\rm F}$ values for P$_{C_{3v}}$ and P$_{D_{2d}}$ patterns are 7.01 eV and 7.02 eV, respectively, which are similar to the result (7.15 eV) reported in the literature.[40] In addition, the $E_{\rm F}$ values are larger than that for the N$_{\rm sub}$ case, implying that the formation of N$_{\rm sub}$ in diamond is energetically more favorable. For both the N and P doping cases, the calculated $E_{\rm F}$ values are positive, meaning that introducing dopants in the host are energetically endothermic.
cpl-36-11-116101-fig5.png
Fig. 5. (a) The bond lengths and (b) bond angles between P and four adjacent C atoms (named as $d_{{\rm PC}_{i}}$ and $\angle {\rm C}_{i}{\rm PC}_{j}$, $i$, $j=1$, 2, 3 and 4) as a function of MD step. The refined structural parameters of P$_{C_{3v}}$ (c) and P$_{D_{2d}}$ (d) in diamond. The partial structural models of P$_{C_{3v}}$ (e) and P$_{D_{2d}}$ (f) in diamond. The brown balls are C atoms, and the red one is a P atom.
The band structures of P$_{\rm sub}$ structures with $C_{3v}$ and $D_{2d}$ symmetries show that the former is spin-degenerated, while partial conduction bands near the Fermi level for the latter are spin-splitting (Figs. 6(a) and 6(b)). Moreover, the donor levels for both doped structures are close to the CBM, suggesting that the P$_{\rm sub}$ in diamond is a shallow donor. The difference between the donor level and the CBM is smaller than that in the literature,[10] which can be further corrected by the Heyd–Scuseria–Ernzerhof hybrid functional.[41] In this work, the relative value is enough comparable to N$_{\rm sub}$ and P$_{\rm sub}$ in diamond. It is found that the donor level is mainly contributed by the P dopant and adjacent four C atoms (Figs. 6(c) and 6(d)). The PDOS further denotes that the contribution of P, C$_{1}$, C$_{2}$, C$_{3}$, C$_{4}$ atoms for the donor level between the two doped structures is similar. Lastly, in Figs. 6(e) and 6(f), the ELF distributions of P$_{\rm sub}$ in diamond with $C_{3v}$ and $D_{2d}$ symmetries are almost the same, and the P atom is four-coordinated with the electrons nearly equally distribute in the four P–C bonds. Noted that it is also similar to that of N$_{\rm sub}$ with $T_{d}$ symmetry (Fig. 3(c)). The radius of N atoms is smaller than that of C atoms, resulting in the N dopant deviated away from the initial substitutional position, while the P atom with a larger radius is almost located in the initial substitutional position. The only effect of substitutional P is to offer one more electron for n-doping and without evident structural distortion, thus a shallow donor is obtained. Consequently, it is expected that the dopant with a similar effect is a good donor. However, the dopant with a too larger atomic radius also means the low doping concentration.
cpl-36-11-116101-fig6.png
Fig. 6. The band structures, total DOS and PDOS of P, C$_{1}$, C$_{2}$, C$_{3}$ and C$_{4}$ atoms and partial ELF of substitutional P in diamond [(a), (c), (e)] with $C_{3v}$ symmetry, and [(b), (d), (f)] with $D_{2d}$ symmetry. The black and red lines are the spin-up and spin-down band structures.
In summary, the structural models of N$_{\rm sub}$ and P$_{\rm sub}$ in diamond are studied by MD simulations and DFT optimizations. The N$_{\rm sub}$ with the $C_{3v}$ symmetry is more stable, while the P$_{\rm sub}$ with $C_{3v}$ and $D_{2d}$ symmetries have the comparative total energies. A shallow (deep) donor level is obtained in P$_{\rm sub}$ (N$_{\rm sub}$) in the diamond structure, which is related to the nearly initial substitutional position for the P atom (the serious deviation of N dopant) after optimization. This is attributed by the atomic radius in the sequence of P$>$C$>$N. Our results may provide a guidance to theoretical study and experimental validation of shallow n-type donors in diamond. References Excitation Spectrum of Aluminum Acceptors in Diamond under Uniaxial StressTheoretical study of Li and Na as n -type dopants for diamondLithium implanted into diamond: Regular trends and anomaliesShallow donors in diamond: Be and MgElectron-Spin Resonance of Nitrogen Donors in DiamondNitrogen and potential n -type dopants in diamondField emission enhancement in nitrogen-ion-implanted ultrananocrystalline diamond filmsAb initio calculation of the structural and elastic properties, anisotropy, and hardness of nitrogen-doped diamondElectronic Structure and N-Type Doping in Diamond from First PrinciplesPulsed EPR studies of Phosphorus shallow donors in diamond and SiCPhosphorus-Related Complexes and Shallow Doping in DiamondConduction in ion-implanted single-crystal diamondOn the substitutional nitrogen donor in diamondn-type conductivity and phase transition in ultrananocrystalline diamond films by oxygen ion implantation and annealingSulfur: A donor dopant for n -type diamond semiconductorsShallow Donors in Diamond: Chalcogens, Pnictogens, and their Hydrogen ComplexesDFT study of halogen impurity in diamondMechanism of high n -type conduction in nitrogen-doped nanocrystalline diamondAtomistic modeling of the polarization of nitrogen centers in diamond due to growth surface orientationComputational models of the single substitutional nitrogen atom in diamondElectronic transitions of electrons bound to phosphorus donors in diamondSymmetry of the phosphorus donor in diamond from first principlesToward highly conductive n-type diamond: Incremental phosphorus-donor concentrations assisted by surface migration of admoleculesn-type doping of (001)-oriented single-crystalline diamond by phosphorusUltraviolet Emission from a Diamond pn JunctionProjector augmented-wave methodEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleMetric-tensor flexible-cell algorithm for isothermal–isobaric molecular dynamics simulationsMulti-impurity complexes for n-type diamond: a computational studyAccurate gap levels and their role in the reliability of other calculated defect propertiesA first principles study of lithium, sodium and aluminum in diamondN-type B-S co-doping and S doping in diamond from first principlesStructural model of substitutional sulfur in diamondFormation of NV centers in diamond: A theoretical study based on calculated transitions and migration of nitrogen and vacancy related defectsEntanglement of quantum node based on hybrid system of diamond nitrogen-vacancy center spin ensembles and superconducting quantum circuitsCould one make a diamond-based quantum computer?Ab Initio Study for Site Symmetry of Phosphorus-Doped DiamondDesign of Shallow Donor Levels in Diamond by Isovalent-Donor CouplingHybrid functionals based on a screened Coulomb potential
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