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Article

P-2B Co-Doping Effects of the Electronic and Optical Properties of Diamond: A First-Principles Study Based on the HSE06 Generalized Function

by
Weiyin Li
1,2,3,* and
Meng Wang
1,2,3
1
School of Electrical and Information Engineering, North Minzu University, Yinchuan 750021, China
2
Key Laboratory of Physics and Photoelectric Information Functional Materials, North Minzu University, Yinchuan 750021, China
3
Microelectronics and Solid-State Electronics Device Research Center, North Minzu University, Yinchuan 750021, China
*
Author to whom correspondence should be addressed.
Crystals 2025, 15(8), 678; https://doi.org/10.3390/cryst15080678
Submission received: 28 May 2025 / Revised: 23 July 2025 / Accepted: 23 July 2025 / Published: 25 July 2025
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Abstract

In the present study, the electronic structure and optical properties of P-2B co-doped diamond have been analyzed using first-principles calculations based on HSE06 generalized functions. Of the 15 complexes that we considered, the five most stable structures—BCPCB system, PCCBCB system, PCBCCB system, PCBBCB system, and PBCB system were identified and studied, and the bandgap was found to reduce from 5.496 eV of intrinsic diamond to 3.610, 3.210, 3.210, 3.210, and 3.250 eV, respectively. Notably, the BCPCB-doped system exhibited significant changes in optical properties: the static dielectric constant increased from 4.18 to over 45, the real part of the conductivity showed a new peak at 2.0 eV (11) with a red-shifted spectrum, the light absorption edge was red-shifted, the static refractive index rose from 2 to 25, and a pronounced peak at 2.5 eV (16) was observed. These theoretical studies aim to support experimental research on P-2B doping in diamond to achieve p-type conductivity and enhanced optical properties.

1. Introduction

Diamond is one of the fourth generation of ultra-wideband semiconductor materials, with high carrier mobility, excellent thermal conductivity, a sizable turn-off voltage, an ultra-wide band gap of 5.45 eV, high breakdown field strength, and chemical stability [1,2,3]. These properties collectively render diamond highly suitable for a spectrum of applications, including photodetection, high-mobility transistors, and solar cells [4,5,6], which are important in advancing the frontiers of optoelectronics and semiconductor science. However, despite its promise for use in electronics, including photodetection, there is a significant gap in knowledge about its application in such devices [7], giving rise to a need for further research. Both natural and synthetic diamonds are insulators, due to their broad bandgap, meaning that doping is required for transition to a semiconductor [8], a process that aims to improve their semiconducting and optical properties. The high activation energies of the primary dopants, which are boron (B) for p-type [9] and phosphorus (P) for n-type [10], with values of approximately 370 meV and 570 meV, respectively, and their low ionization rates in diamond, present considerable obstacles to effective doping [11,12]. A wealth of theoretical studies and experimental research has led to the achievement of n-type conductivity in diamond, and this technology is maturing steadily [13,14,15,16]. In contrast, the development of p-type conductive diamond is lagging, primarily due to the scarcity of research on acceptor impurities. To induce p-type conductivity, a range of monomers and compounds have been investigated, including oxides such as NO2 and MoO3 [17,18,19], in which oxygen termination is employed to create p-type diamond semiconductors [20]. In addition, there have been attempts to dope diamond with group III elements, such as boron (B), aluminum (Al), and gallium (Ga), and group IV elements such as silicon (Si) [21]. Of these materials, boron stands out as the most promising acceptor in diamond due to its lower predicted acceptor level [22]. However, the limited solubility of boron in monodoping has impeded the development of low-resistance p-type diamonds. Furthermore, the possible applications of diamond in electronic devices, and particularly in photodetection, remain underexplored, underscoring the need for further research into the potential uses of diamond in these advanced applications.
In recent years, many theoretical studies have shown that a donor-acceptor co-doping strategy is an effective way to fabricate low-resistance p-type diamonds and can also improve the optical properties of diamond. This approach is expected to offer a universal means of valence modulation, thus helping to solve the self-compensation challenges prevalent in wide bandgap and ultra-wide bandgap semiconductors [23,24]. Sun et al. [25] calculated different ratio models for B and S co-doping and concluded that for B and S ratios above 2:1, a transition occurs from n-type to p-type co-doped diamonds. Li et al. [26] found that B and H co-doped diamonds have more compatible lattice structures than B-doped diamonds, that co-doped diamonds exhibit p-type semiconductor behavior, and that the carrier concentration and conductivity of co-doped diamonds are higher than for B-doped diamond crystals. Zhang et al. [27] experimentally obtained B-S co-doped Ib-type large N-type diamonds with values for the resistivity and Hall mobility of 8.510 Ω·cm and 760.870 cm2/V·s, respectively. Li et al. [28] found that B doping helps to improve the electrical conductivity and optical properties of B-S doped diamond. Konov et al. [29] conducted an experiment that yielded the conclusion that boron-doped diamond has a positive effect on electron mobility. Kunuku et al. [30] demonstrated the enhancement of electrical conductivity through boron–nitrogen co-doping of diamond and achieved attractive high-quality and low-resistivity layers. Wang et al. [31] realized n-type semiconductors using FeS singly doped diamond and B-S co-doped diamond, and demonstrated that B-FeS co-doping helps to increase the Hall mobility and carrier density and reduces resistance. Fan et al. [32] achieved n-type conductivity in diamond with ionization energies as low as 109 meV using a boron–phosphorus co-doping scheme with diamond nuggets; however, their study did not cover the optical properties of these systems, so, in the present study, the optical properties of P-2B complex-doped diamond systems are investigated in detail. While researchers have established a basic understanding of co-doped diamond, the specific structures of diamonds co-doped with two elements (for example, P and B) remain unclear, and their electronic and optical properties are also not well understood.
Consequently, the structures of P-2B complex-doped diamond were first determined, and then their electronic and optical properties were investigated using first principles [33]. The theoretical studies presented here are designed to lay the groundwork for experimental investigations into the doping of diamond with P-2B complexes, with the goal of achieving p-type conductivity and enhanced optical properties.

2. Calculation Methods

In this study, all calculations were performed using the CASTEP [34] computational package within Materials Studio 2019, employing the generalized gradient approximation (GGA) and the Perdew–Burke–Ernzerhof (PBE) [35] exchange–correlation functional under DFT. To improve the precision of energy band structure calculations of the intrinsic diamond and P-2B doped systems, the HSE06 [36] generalized functions were used for their electronic structures. The OTFG ultra-soft pseudopotential was applied to describe the interaction of valence electrons with the atomic reality in geometry-optimized structural calculations. To ensure the accuracy of the findings, an in-depth analysis of the total energy variation for endogenous diamond and the three doping systems in relation to the cutoff energy was conducted, with the results presented in Figure 1. The analysis showed that the total energy for all four systems consistently decreased as the cutoff energy was raised. More specifically, it was observed that the total energy stabilized at a cutoff energy of 750 eV and remained constant from 800 eV onward. The Brillouin zone integral is calculated using a 2 × 2 × 2 K-point grid. The geometry-optimized inter-atomic force convergence threshold was set to 0.003 eV·nm−1, with an atomic displacement convergence threshold of 0.0001 nm and a system total energy change convergence threshold of 1 × 10−5 eV. The interatomic internal stress convergence threshold was 0.05 GPa, and the Broyden–Fletcher–Goldfarb-Shanno [37] algorithm was chosen for geometry optimization, with calculations performed in the inverse easy space. The valence electrons for C, P, and B atoms were considered to be C-2s22p2, P-3s23p3, and B-2s22p, respectively.

3. Results and Discussion

3.1. Intrinsic Diamond

The energy band structure of intrinsic diamond, obtained from a first-principles study using the aforementioned parameters, is depicted in Figure 1, along with the total and partial densities of states. As illustrated in Figure 2a, the bandgap of intrinsic diamond is calculated as 5.496 eV, which closely matches the experimental value of 5.45 eV. The conduction and valence band extrema are not at the same point, showing that diamond is an indirect band gap semiconductor. As illustrated in Figure 2, the electronic states in proximity to the Fermi level are predominantly 2p states of carbon atoms. In the energy range of 5.469–20 eV, the electronic states are mainly contributed by the 2p states, with a minor contribution from the 2s states of carbon atoms. In the energy range of −15 to −20 eV, the electronic states are predominantly contributed by the 2s states of carbon atoms. The close agreement between these calculated results and the experimental values further validates the accuracy of our calculations [1].

3.2. Determination of the Doping Structure

In the process of constructing the model, we considered two distinct scenarios: the first involved positioning the phosphorus (P) atom between two boron (B) atoms, forming a B-P-2B configuration, while the second involved a P-2B-B arrangement. For each of these scenarios, we varied the number of carbon atoms between the P and B atoms or between the B atoms. Configurations with more than two carbon atoms between P and B or between B and B were not considered complex, so we limited our examination to 15 cases, of which the 5 with the lowest energy are presented in Figure 3, while the remaining configurations are described in the Supplementary Materials.
In order to assess the chemical stability of the P-2B complexes and to determine the most favorable configuration, we calculated the total energies of 15 P-2B complex-doped systems using first-principles studies. As shown in Table 1, the total energies of the doped complex systems with neighboring B-B sites are generally higher than for the B-B complexes separated by C or P. After comparing all the doped systems, we selected the five systems with the lowest formation energies (EBCPCB = −10288.7557 eV, EPCCBCCB = −10288.5303 eV, EPCBCCB = −10288.5903 eV, EPCBCB = −10288.4332 eV, and EPBCB = −10288.4071 eV) for further calculation and discussion.

3.3. Electronic Structure

3.3.1. Band Structure

The electrical properties of P-2B co-doped diamond were reasonably predicted by a first-principles study based on density-functional theory, and the electronic energy band structure of P-2B co-doped diamond with a good structure was simulated. From an analysis of Figure 2 and Figure 4, it is clear that the forbidden bandwidths for all the P-2B composite doped diamond systems are lower than for intrinsic diamond, and are reduced from 5.496 eV to 3.610 eV (BCPCB system), 3.210 eV (PCCBCCB system), 3.210 eV (PCBCCB system), 3.100 eV (PCBBCB system), and 3.250 eV (PBCB system). While the bandwidth has decreased, the highest valence band point and lowest conduction band point in all doped systems are still not at the K point. So, these systems remain indirect band gap semiconductors. Further comparison of Figure 2 and Figure 4 shows that adding P-B complexes creates new energy levels near the valence band maximum. These new levels make the Fermi level (Ef) shift from the band middle to near the valence band top. The partial emptiness of these newly formed bands is the main reason for p-type doping.
To validate the study’s accuracy, the electronic structure of 2P-B-doped diamond from reference [32] was used for comparison. The 2P-B-doped diamond in reference [32] is n-type, whereas the 2B-P-doped diamond in this study is p-type, aligning with composite regularity, and both B-2P and P-2B-doped diamonds exhibit a reduced band gap and increased conductivity.

3.3.2. Density of States

Figure 2c and Figure 3b show that the peaks between −20 and 10 eV come from the 2s and 2p states of carbon atoms. Most of the peaks from −10 to 0 eV are due to the 2p states of carbon atoms. There are no electronic states in the range zero to 5.496 eV, which corresponds precisely to the bandgap of 5.496 eV in the energy band structure. The peaks from 5.496 to 20 eV are primarily from the 2p states of C atoms, with some from the 2s states of C atoms.
The TDOS and PDOS for P-2B complexes co-doped with diamond were calculated in a similar manner. As shown in Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, there are some commonalities among these five configurations. Firstly, it is evident that the 3p state of the P atom primarily contributes to the bottom of the conduction band, and the Fermi energy level is near the top of the valence band, indicating p-type conductance. Secondly, the impurity energy levels shown in Figure 3 mainly originate from the 2p state and a few 2s states of the B atoms, while the top of the valence band is primarily formed by the hybridization of the 2p state of the C atoms, the 3p state of the P atom, and the 2p state of the B atoms, with the main contribution coming from the B atoms. Thirdly, all Fermi energy levels pass through the impurity states near the top of the valence band. These results lead us to conclude that the impurity state is typically the acceptor state, suggesting that all five P-2B complex-doped systems are p-type semiconductors.

3.4. Optical Properties

The optical properties of diamond arising from changes in the electronic energy band structure were computationally analyzed after doping with P-2B complexes to elucidate the effects in terms of dielectric function [38], conductivity, absorption, reflection, and energy loss, and to reveal the mechanisms behind these changes.

3.4.1. Dielectric Functions

The real part of the dielectric function, denoted as ε 1 ω , correlates with the energy stored within the material. The imaginary part, represented by ε 2 ω , is associated with energy loss or the light absorption ratio, which is decomposed into real and imaginary components and can be mathematically articulated as follows:   ε ω = ε 1 ( ω ) + ε 2 ( ω ) j . Figure 10a,b illustrate the real and imaginary parts of the dielectric function for the intrinsic, BCPCB-doped system, and the other four doped systems.
As illustrated in Figure 10a, the BCPCB-doped diamond system, when compared to intrinsic diamond and four other complex-doped diamond systems, displays notable variations in the real component of the dielectric function across the low-energy spectrum. Specifically, within the frequency band below 0.25 THz, the real component of the dielectric function for the BCPCB-doped system is considerably elevated compared to that of pure diamond and the other four complex-doped systems. However, within the frequency range of 0.25 to 1.5 THz, the real component of the dielectric function for the BCPCB-doped system is lower than the other systems, yet all five doped systems exceed the intrinsic diamond. The static dielectric constant for pure diamond is recorded at 4.18, for the BCPCB-doped system it is 45, and for the other four complex-doped diamond systems, it falls roughly between 7.5 and 12.5. This enhancement in static dielectric constants across the five complex-doped diamond systems in the low-energy region bolsters predictive accuracy and intensifies the electromagnetic interactions within the photonic field, thus fostering carrier migration [39]. Consequently, the integration of P-2B composites into photonic device design can attain the requisite electrostatic dielectric constants.
As illustrated in Figure 10b, the imaginary component of the dielectric constant for each P-2B-doped diamond system is shifted to the left, indicating a low-energy region transition. Notably, the BCPCB-doped diamond system exhibits a value significantly higher than the other four complex-doped systems at zero frequency. The frequency is represented on the horizontal axis. The imaginary component of the dielectric function for intrinsic diamond peaks at 3.0 and 3.4 THz. In contrast, the BCPCB-doped system peaks at 0.25 and 2.4 THz, followed by the other four doped systems, which exhibit minor variations in the imaginary component of the dielectric function, all peaking at 2.4 THz. It is evident that the BCPCB-doped system has the most pronounced peaks, and these peaks are situated in the low-frequency region (frequency < 2.4 THz). The imaginary component of the dielectric function for the P-2B composite-doped system surpasses that of intrinsic diamond. This observation suggests that the optical intensity jump of the five P-2B composite-doped diamond systems surpasses that of intrinsic diamond. This finding implies that P-2B composite doping may result in a reduction in electron concentration in the low-frequency region of diamond. This reduced frequency demand correlates with an enhanced optical migration of electrons in the low-frequency region of diamond (particularly below 2.4 THz).

3.4.2. Electrical Conductivity

The real part of the complex conductivity reflects the DC conductivity of the material, which is related to the charge carrier concentration and mobility. From Figure 11a, it is evident that the incorporation of P-2B complexes significantly boosts the DC conductivity of diamond within the low-energy spectrum. This improvement is directly linked to the upward movement of the valence band in the doped diamond, which brings it nearer to the Fermi level, thereby extending the energy range within which DC conductivity is manifested, based on the displacement of the valence band and conduction band after doping, it has boron-like characteristics. Notably, within the BCPCB-doping configuration, there is a distinct emergence of a peak at 2.0 eV, suggesting that the BCPCB-doped system can realize DC conductivity at 2eV. All five complexes produce new peaks at 10 and 14 eV, which further indicates that the P-2B complexes can improve the DC conductivity of the system.
In contrast, the imaginary part of the complex conductivity is related to the response of the material to the AC electric field, which involves the optical properties and the electron leaps. From Figure 11b, it can be seen that the BCPCB-doped system has a new peak at 2 eV, indicating that BCPCB can improve the electron transition probability and further improve the optical properties of the system. The values for the five complexes are larger than for intrinsic diamond at E > 10 eV, which suggests that the P-2B complexes can enhance the system’s correlation with the AC electric field and improve the electron transition probability. When compared to the single-doped diamond with B atoms studied by Gajewski et al. [40], the P-2B complex-doped diamond shows higher conductivity. Additionally, its carrier mobility is also enhanced.

3.4.3. Absorption Coefficient and Reflectance

The absorption coefficient shows how much energy is absorbed per unit length of the photon passing through the medium. Figure 12a shows the absorption coefficients for the three systems. The edge of the optical absorption energy band for undoped diamond is at 5.95 eV. After doping with P-2B complex, however, the edge of the absorption energy band is shifted leftward to below 5.95 eV. This shift, or ‘redshift’, makes the doped diamond absorb light over longer wavelengths. In the BCPCB-doping configuration, the emergence of a pronounced peak at 2.0 eV arises from the hybridization of B 2p, P 3p, and C 2p orbitals following incorporation of the P–2B complex. Upward displacement of the valence-band maximum toward the Fermi level consequently lowers the transition energy for electrons. At E > 5 eV, the changes in the absorption coefficients for the remaining four complex-doped systems were not very different from BCPCB, although the BCPCB-doped system had the highest peak.
The results presented above indicate that the absorption spectral range of the system was enlarged by P-2B complex doping, which improved the photocatalytic performance of diamond. The wavelength of light absorption can be obtained by the following equation [41]:
λ = h c / E
where h represents Planck’s constant, c is the speed of light, and E is the energy. Taking the BCPCB-doping system as an example, the absorption coefficient of BCPCB in the lower energy region with a peak value of 2.0 eV is calculated as a wavelength of 620 nm according to Equation (1).
From Figure 12b, it can be seen that the static reflectivity of intrinsic diamond is 0.16, while that of the BCPCB-doped system is 0.85, and the values for the remaining four complex-doped systems do not differ much over the range 0.2–0.3. The reflectivity of the BCPCB-doped system at E < 2.5 eV is higher than for intrinsic diamond and the other four complex-doped systems, while the reflectivity for the BCPCB-doped system at 2.5 eV is significantly lower than the reflectivity of intrinsic diamond, indicating that the BCPCB-doping system has the largest photon transmittance. In addition, at E > 7.5 eV, the changes in reflectance for the five complex doping systems are not very different, with all of the values being higher than for intrinsic diamond in general, and lower than for intrinsic diamond only near 20 eV, although BCPCB still shows the highest peak value.

3.4.4. Refractive Index and Extinction Coefficient

Figure 13a shows the values for the refractive index n of the intrinsic diamond and the P-2B complex-doped diamond systems. It can be observed that the static refractive index of intrinsic diamond is n0 = 2.1, while the value for the BCPCB-doped system is 22.5; the values for the remaining four complex-doped systems do not differ much over the range 2.5–2.7 eV. The refractive index of the BCPCB-doped system at E < 2eV is higher than that of the other systems, indicating that doping with BCPCB can enhance the transmittance of diamond.
Extinction coefficients (k) show the extent of light absorption, as demonstrated in Figure 13b for intrinsic diamond and the five doped systems. The figure shows that P-2B complexes shift extinction coefficients towards lower energies. The maximal intrinsic value is 15 eV (k = 2.63). The P-2B complexes’ extinction coefficients are larger than the intrinsic diamond, showing that doping with P-2B complexes can improve light absorption. The peak value for the BCPCB-doped system appears at 2 eV, with a value of 9; this is much larger than for intrinsic diamond and the other four complex-doped systems, indicating that the BCPCB-doping system has the strongest light absorption at E = 2 eV, corresponding to a change in its absorption coefficient.

3.4.5. Energy Loss Spectroscopy

Figure 14 shows the energy loss spectra for the intrinsic diamond and P-2B complex-doped diamond systems. It can be seen that the P-2B complex doping static can significantly increase the energy loss of the system. BCPCB generates a new peak at E = 2.5 eV, which is much larger than for intrinsic diamond and the rest of the four complex-doped systems, indicating that there is a significant decrease in the energy of the photons transmitted through the lower energy region of the BCPCB; this means that the absorption coefficient of the BCPCB-doped system at 2.5 eV increases, a finding that is consistent with the analysis of the absorption and extinction coefficients.

4. Conclusions

The effects of P-2B complexes on the electronic and optical characteristics of diamond have been studied. First-principles density functional theory calculations were employed for this purpose, in conjunction with the GGA/PBE and HSE06 methods. Doping with five P-2B complexes notably reduced diamond’s bandgap, from 5.496 eV to 3.610–3.250 eV, due to impurity levels in the conduction band from interatomic interactions. This shifted the Fermi level near the valence band top, causing p-type doping from the new bands’ partial vacancy. The absorption band edge moved to lower energies, with the BCPCB-doped system showing a 620 nm (2.0 eV) absorption peak. P-2B doping also enhanced optical properties like dielectric constant, conductivity, refractive index, reflectivity, and extinction coefficient at lower energies. The static dielectric constant rose from 4.18 to 45, and conductivity jumped to boost carrier mobility in the BCPCB system. The static refractive index rose from 0.18 to 0.85, and static reflectance from 2 to 23. The energy loss peak shifted to lower energies with a higher value post-doping, and a new peak emerged near 2.5 eV, indicating stronger light absorption. These findings suggest P-2B complex doping significantly impacts diamond’s electronic and optical properties, offering a theoretical basis for diamond’s use in semiconductors.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/cryst15080678/s1, Figure S1: The structure of PBCB doped system; Figure S2: The structure of BPCP doped system; Figure S3: The structure of BCCPCB doped system; Figure S4: The structure of PBB doped system; Figure S5: The structure of PCCBB doped system; Figure S6: The structure of BPB doped system; Figure S7: The structure of PCBB doped system; Figure S8: The structure of BCCPB doped system; Figure S9: The structure of PCCBCB doped system; Figure S10: The structure of BCPCB doped system; Figure S11: The structure of PCBCB doped system; Figure S12: The structure of PCBCCB doped system; Figure S13: The structure of BCCPCCB doped system; Figure S14: The structure of PBCCB doped system; Figure S15:The structure of PCCBCCB doped system.

Author Contributions

Conceptualization, W.L. and M.W.; Software, W.L.; Investigation, W.L. and M.W.; Writing—Original Draft, M.W.; Writing—Review and Editing, W.L. and M.W.; Funding Acquisition, W.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Foundation of Ningxia (Grant Nos. 2023AAC03318 and 2022AAC03267), the National Natural Science Foundation of China (Grant Nos. 11764001), the High Level Talent Project of North Minzu University (Grant No. 2019BGGZ08), the Ningxia new solid electronic materials and devices research and development innovation team (Grant No. 2020CXTDLX12), and the Fundamental Research Funds for the Central Universities, North Minzu University (Grant No. 2022XYZDX03), 2025 Year National College Student Innovation and Entrepreneurship Training Program Project (Grant No. 202511407003).

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Figure 1. The relationship between changes in total energy of each system with the increase in cutoff energy value, dashed lines indicate energy convergence.
Figure 1. The relationship between changes in total energy of each system with the increase in cutoff energy value, dashed lines indicate energy convergence.
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Figure 2. Band structure (a), total density of states (b), and partial wave density of states (c) of the intrinsic diamond.
Figure 2. Band structure (a), total density of states (b), and partial wave density of states (c) of the intrinsic diamond.
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Figure 3. The five structures with the lowest energy in the P-2B complex doping system of 64-atom diamond supercell. (a) BCPCB; (b) PCCBCCB; (c) PCBCCB; (d) PCBCB; (e) PBCB. Due to the diverse structures of P-2B complexes, the standard explanation is as follows. Firstly, we categorize them into two types. One is when two boron atoms are separated by a phosphorus atom (i.e., B-P-B), and the other is when two boron atoms are adjacent and the phosphorus atom is attached to one of the boron atoms (i.e., B-B-P). Then, in each category, we further consider the number of carbon atoms between the P-B and B-B bonds. From this figure, it can be seen that we have chosen a suitable perspective to clearly observe the visualization configuration. For example, we name the configuration in Figure 2a BCPCB, which means there is a carbon atom between B and P. The configuration in Figure 2b is PCCCBCCB, which means there are two carbon atoms between B and P, as well as between P and P. Note that we only consider the second closest distance between B-P and P-P, because due to the size of the superlattice we construct, the composite with the third adjacent B-P or P-P will be considered as another composite considering periodic boundary conditions. For example, BPCCBB is actually PBCCCB.
Figure 3. The five structures with the lowest energy in the P-2B complex doping system of 64-atom diamond supercell. (a) BCPCB; (b) PCCBCCB; (c) PCBCCB; (d) PCBCB; (e) PBCB. Due to the diverse structures of P-2B complexes, the standard explanation is as follows. Firstly, we categorize them into two types. One is when two boron atoms are separated by a phosphorus atom (i.e., B-P-B), and the other is when two boron atoms are adjacent and the phosphorus atom is attached to one of the boron atoms (i.e., B-B-P). Then, in each category, we further consider the number of carbon atoms between the P-B and B-B bonds. From this figure, it can be seen that we have chosen a suitable perspective to clearly observe the visualization configuration. For example, we name the configuration in Figure 2a BCPCB, which means there is a carbon atom between B and P. The configuration in Figure 2b is PCCCBCCB, which means there are two carbon atoms between B and P, as well as between P and P. Note that we only consider the second closest distance between B-P and P-P, because due to the size of the superlattice we construct, the composite with the third adjacent B-P or P-P will be considered as another composite considering periodic boundary conditions. For example, BPCCBB is actually PBCCCB.
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Figure 4. Band structure of five doping systems. (a) BCPCB; (b) PCCBCCB; (c) PCBCCB; (d) PCBCB; (e) PBCB.
Figure 4. Band structure of five doping systems. (a) BCPCB; (b) PCCBCCB; (c) PCBCCB; (d) PCBCB; (e) PBCB.
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Figure 5. TDOS and PDOS of the BCPCB system. (a) TDOS of BCPCB system; (b) PDOS of the C atom in the BCPCB system; (c) PDOS of the P atom in the BCPCB system; (d) PDOS of the B atom in the BCPCB system.
Figure 5. TDOS and PDOS of the BCPCB system. (a) TDOS of BCPCB system; (b) PDOS of the C atom in the BCPCB system; (c) PDOS of the P atom in the BCPCB system; (d) PDOS of the B atom in the BCPCB system.
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Figure 6. TDOS and PDOS of the PCCBCCB system. (a) TDOS of PCCBCCB system; (b) PDOS of the C atom in the PCCBCCB system; (c) PDOS of the P atom in the PCCBCCB system; (d) PDOS of the B atom in the PCCBCCB system.
Figure 6. TDOS and PDOS of the PCCBCCB system. (a) TDOS of PCCBCCB system; (b) PDOS of the C atom in the PCCBCCB system; (c) PDOS of the P atom in the PCCBCCB system; (d) PDOS of the B atom in the PCCBCCB system.
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Figure 7. TDOS and PDOS of the PCBCCB system. (a) TDOS of PCBCCB system; (b) PDOS of the C atom in the PCBCCB system; (c) PDOS of the P atom in the PCBCCB system; (d) PDOS of the B atom in the PCBCCB system.
Figure 7. TDOS and PDOS of the PCBCCB system. (a) TDOS of PCBCCB system; (b) PDOS of the C atom in the PCBCCB system; (c) PDOS of the P atom in the PCBCCB system; (d) PDOS of the B atom in the PCBCCB system.
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Figure 8. TDOS and PDOS of the PCBCB system. (a) TDOS of PCBCB system; (b) PDOS of the C atom in the PCBCCB system; (c) PDOS of the P atom in the PCBCB system; (d) PDOS of the B atom in the PCBCB system.
Figure 8. TDOS and PDOS of the PCBCB system. (a) TDOS of PCBCB system; (b) PDOS of the C atom in the PCBCCB system; (c) PDOS of the P atom in the PCBCB system; (d) PDOS of the B atom in the PCBCB system.
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Figure 9. TDOS and PDOS of the PBCB system. (a) TDOS of PBCB system; (b) PDOS of the C atom in the PBCB system; (c) PDOS of the P atom in the PBCB system; (d) PDOS of the B atom in the PBCB system.
Figure 9. TDOS and PDOS of the PBCB system. (a) TDOS of PBCB system; (b) PDOS of the C atom in the PBCB system; (c) PDOS of the P atom in the PBCB system; (d) PDOS of the B atom in the PBCB system.
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Figure 10. Dielectric functions of intrinsic diamond and P-B complex-doped diamond systems (a) real part and (b) imaginary part.
Figure 10. Dielectric functions of intrinsic diamond and P-B complex-doped diamond systems (a) real part and (b) imaginary part.
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Figure 11. Electrical conductivity of intrinsic diamond and diamond systems doped with P-B complexes (a) real and (b) imaginary.
Figure 11. Electrical conductivity of intrinsic diamond and diamond systems doped with P-B complexes (a) real and (b) imaginary.
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Figure 12. (a) Absorption coefficient and (b) reflectance of intrinsic diamond and diamond systems doped with P-B complexes.
Figure 12. (a) Absorption coefficient and (b) reflectance of intrinsic diamond and diamond systems doped with P-B complexes.
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Figure 13. (a) Refractive index and (b) extinction coefficient of intrinsic diamond and P-B complex-doped diamond systems.
Figure 13. (a) Refractive index and (b) extinction coefficient of intrinsic diamond and P-B complex-doped diamond systems.
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Figure 14. Energy loss in intrinsic diamond and diamond systems doped with P-B complexes.
Figure 14. Energy loss in intrinsic diamond and diamond systems doped with P-B complexes.
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Table 1. The total energy of the considered P-2B complex. The left column lists the formation energy of a complex where two B atoms are separated by a P atom. The right column lists the total energy of a complex with two adjacent B atoms and a P atom located on one side of the B atom. In each column, different numbers of carbon atoms between B-P and/or P-P bonds are considered, for a total of fifteen cases.
Table 1. The total energy of the considered P-2B complex. The left column lists the formation energy of a complex where two B atoms are separated by a P atom. The right column lists the total energy of a complex with two adjacent B atoms and a P atom located on one side of the B atom. In each column, different numbers of carbon atoms between B-P and/or P-P bonds are considered, for a total of fifteen cases.
ComplexTotal Energy (eV)ComplexTotal Energy (eV)
BPB−10288.2448PBB−10287.9116
BPCB−10288.2525PCBB−10288.0739
BPCCB−10288.2836PCCBB−10287.6711
BCPCB−10288.7557PBCB−10288.4071
BCPCCB−10288.4520PCBCB−10288.4332
BCCPCCB−10288.1217PCCBCB−10288.2628
PBCCB−10288.2050
PCBCCB−10288.5903
PCCBCCB−10288.5303
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Li, W.; Wang, M. P-2B Co-Doping Effects of the Electronic and Optical Properties of Diamond: A First-Principles Study Based on the HSE06 Generalized Function. Crystals 2025, 15, 678. https://doi.org/10.3390/cryst15080678

AMA Style

Li W, Wang M. P-2B Co-Doping Effects of the Electronic and Optical Properties of Diamond: A First-Principles Study Based on the HSE06 Generalized Function. Crystals. 2025; 15(8):678. https://doi.org/10.3390/cryst15080678

Chicago/Turabian Style

Li, Weiyin, and Meng Wang. 2025. "P-2B Co-Doping Effects of the Electronic and Optical Properties of Diamond: A First-Principles Study Based on the HSE06 Generalized Function" Crystals 15, no. 8: 678. https://doi.org/10.3390/cryst15080678

APA Style

Li, W., & Wang, M. (2025). P-2B Co-Doping Effects of the Electronic and Optical Properties of Diamond: A First-Principles Study Based on the HSE06 Generalized Function. Crystals, 15(8), 678. https://doi.org/10.3390/cryst15080678

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