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The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D blue phosphorene: A dispersion corrected DFT study
Journal Pre-proof The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D blue phosphorene: A dispersion corrected DFT study R.M. Arif Khalil, Fayyaz Hussain, Muhammad Iqbal Hussain, Afshan Perveen, Muhammad Imran, G. Murtaza, M.A. Sattar, Anwar Manzoor Rana, Sungjun Kim PII:
S0925-8388(20)30618-6
DOI:
https://doi.org/10.1016/j.jallcom.2020.154255
Reference:
JALCOM 154255
To appear in:
Journal of Alloys and Compounds
Received Date: 26 November 2019 Revised Date:
6 February 2020
Accepted Date: 9 February 2020
Please cite this article as: R.M.A. Khalil, F. Hussain, M.I. Hussain, A. Perveen, M. Imran, G. Murtaza, M.A. Sattar, A.M. Rana, S. Kim, The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D blue phosphorene: A dispersion corrected DFT study, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/j.jallcom.2020.154255. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
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CREDIT AUTHOR STATEMENT Dear Editor, With reference to Ms. Ref. No.: JALCOM-D-19-15442, we are resubmitting our manuscript titled “The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study”. All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in the Journal of Alloys and Compounds. Authors Contributions Conceptualization, R. M. Arif Khalil, Afshan Perveen; Methodology, Muhammad Iqbal Hussain; Software, Fayyaz Hussain; Validation, R. M. Arif Khalil, Fayyaz Hussain and Muhammad Iqbal Hussain; Formal Analysis, Afshan Perveen, Muhammad Iqbal Hussain; Investigation, Muhammad Iqbal Hussain; Resources, R. M. Arif Khalil; Data Curation, Muhammad Iqbal Hussain; WritingOriginal Draft Preparation, Muhammad Iqbal Hussain, R. M. Arif Khalil; Writing-Review & Editing, Muhammad Iqbal Hussain, R. M. Arif Khalil, Fayyaz Hussain, Muhammad Imran, Anwar Manzoor Rana, Ghulam Murtaza. M. Atif Sattar and Sungjun Kim Visualization, R. M. Arif Khalil and Muhammad Iqbal Hussain; Supervision, R. M. Arif Khalil; Project Administration, R. M. Arif Khalil; Funding Acquisition, No.
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Dr. Rana M. Arif Khalil Assistant Professor Department of Physics Bahauddin Zakariya University Multan Pakistan Dr. Fayyaz Hussain Assistant Professor Department of Physics Bahauddin Zakariya University Multan Pakistan
The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study. R. M. Arif Khalila*, Fayyaz Hussaina*, Muhammad Iqbal Hussaina,b, Afshan Perveena, Muhammad Imranc, G. Murtazad, M. A. Sattare, Anwar Manzoor Ranaa and Sungjun Kimf a Materials Simulation Research Laboratory (MSRL), Department of Physics, Bahauddin Zakariya University Multan, 60800, Pakistan b Department of Physics, University of Education, Lahore, 54000, Pakistan c Department of Physics, Govt. College University Faisalabad, Pakistan, 38000, Pakistan d Center of Advanced Studies in Physics (CASP), GC University, Lahore, 54000, Pakistan e Physics Department, College of Science, United Arab Emirates University, Al Ain, UAE f School of Electronics Engineering Chungbuk National University Cheongju 28644, South Korea
Corresponding Email*:[email protected], [email protected]
Abstract The present study has been performed to investigate optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP using the Cambridge Serial Total Energy Package (CASTEP) simulation code based on the density functional theory (DFT). The optical and vibrational properties were carried out by employing dispersion corrected density functional theory. The calculated lattice constants for pristine blue phosphorene a = b= 3.33 Å are found to be improved by Tkatchenko-Scheffler (TS) and Grimme (G06) schemes for 2D phosphorene. The band structures
and density of states results have figured out indirect band gaps as 1.93eV (pristine), 0.35eV (with single vacancy), 0.37eV (Ce doped), 0.68eV (Ti doped), and 0.56eV (Ti-Ti doped) in blue phosphorene. Whereas, no band gap has been observed for Ce-Ce doped blue phosphorene. The phonon dispersion curves obtained by density functional theory perturbation theory presented dynamical stability of the studied materials without any imaginary modes of phonon spectra. The Raman active optical modes of vibrations are found at the highest frequency of 520 cm-1. The Spin polarized density of states portray that (Ce, Ti, Ti-Ti) doped blue phosphorene exhibit semi-metallic like behavior due to hybridization of 4f, 5d and 3d localized energy states. The optical properties show that the plasma frequencies occurred at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) blue phosphorene. Moreover, significant shift of absorption peak towards high energy range is clear signature of the blue shift.
Keywords: 2D Blue Phosphorene, Dispersion correction, dynamical, phosphorene, Hubbard, spin polarized
1.
Introduction Nowadays, two dimensional (2D) materials are gaining considerable attention of
researchers due to their fascinating characteristics like electronic, optical and many others [15]. It is obvious that spin electronic appliances need identification and generation of spin electronic current, which can preferably be done using ferromagnetic semiconductors. Thus, most of the 2D materials are non-magnetic in nature [6-9]. The discovery of the graphene [10, 11], which belongs to 2D family, had open new horizons to explore and categorize numerous other 2D materials, e.g., MOS2 [12, 13] BN [14], Silicone [15], g-C3N4 [16, 17] and graphyne [18-20], etc. Besides, layered phosphorous (black phosphorene) has also been victoriously isolated through mechanical peeling from the bulk phosphorous [21-23]. It has attracted much attentions over the last few years due to its direct band gap 1.51 eV at room temperature with high mobility carriers (103 cm2 v-1 s-1) and its current on/off ratio about 104. All these magnificent features have made black phosphorene a marvelous, attractive and piquant 2D material which is a potential candidate to be utilized in optical and nano electronics tools. Tomanek et al. are pioneers who predicted blue phosphorene in 2014 as an allotrope of black phosphorene which was synthesized successfully by Zhenyu Li et al. [24, 25] from the epitaxial development on Au (111) utilizing the black phosphorene as precursor. It has honeycomb like structure similar to that of graphene. It is stable at room temperature as that of black phosphorene [26]. It has indirect band gap 2 eV [27] which makes it another optimistic allotrope of the phosphorous for its applications in nano electronic tools. Furthermore, the theoretical predictions reveal that blue phosphorene ought to be exfoliating smoothly to make quasi thin 2D patterns, which is suitable for application in nano-electronic devices [26]. To expose physical properties for the semi metallicity, Due et al. presented a model and anticipated that Fe, Co and Cr doped graphene show their behavior like semi metallic ferromagnetic [28]. Hong et al. described that substitution of Cr, Mn and Ti on black phosphorene results spin polarized semiconducting state while semi metallic state was
observed by doping either V or Fe [29]. Recently, some theoretical investigations have been made on substitutionally doping in blue phosphorene to revise its properties. Tang et al. found band gap of C and O substituted blue phosphorene [30]. They also observed that Sb and Al dopants in blue phosphorene lead transition from indirect to direct band gap. The doping Si in blue phosphorene results diluted magnetic semiconductor (DMS) like property [31]. Cho et al. explained that blue phosphorene doped with 3d transition metals such as Cr, Mn, Fe and V contaminations, Ni dopant exhibits half metallic like character whereas Sc and Co dopants display DMS and non-magnetic behavior [32]. However, up till now, no study has been done to include Van der Waals interactions in the blue phosphorene (BP). These Van der Waals interactions play crucial role to calculate the better properties of 2D BP. In the present work, dispersion corrected optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP are investigated through efficient CASTEP simulation package based on DFT. 2.
Computational Approach The first principles calculations based on density functional theory (DFT) are carried
out to investigate optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP [33, 34]. We opted norm conserving pseudo-potential [35] for these calculations. In addition, the Gaussian smearing value of 0.1 eV, cut-off energy of 540 eV along with Monkhorst–Pack [36] grid of the values 17×17×1 have been used to sample the Brillouin zone. Besides, the conjugate gradient method [37] was selected to relax the ionic positions, cell volume and lattice parameters of the system until the Hellmann Feynman forces [38] found smaller than 0.02 eV/Å and the energy convergence criteria was met at 1×10-5 eV. Perdew Burke and Ernzerhof - generalized gradient approximation (PBE-GGA) [39] has been used to describe exchange and correlation potential within the framework of CASTEP code [40]. Broyden-FletcherGoldfarb-Shannon (BFGS) method has been used for geometry optimization and achievement of optimal accuracy in results [41]. The supercell of size (3 × 3 × 1) containing
18 atoms has been taken for all configurations. Furthermore, DFT+U approach is used for magnetic calculations [42]. The vibrational behavior has been observed through finite displacement method [43, 44]. To improve the structural and vibrational properties, dispersion corrections TS [45] and G06 [46] schemes are incorporated along with exchange and correlation functional. However, the magnetic and optical calculations are performed using better dispersion corrected TS scheme. 3. 3.1
Results and Discussion Structural and electronic properties The crystal structures of pristine blue phosphorene, (Ce, Ce-Ce, Ti, Ti-Ti) doped blue
phosphorene and with singe vacancy in blue phosphorene are shown in figures (1 and 2). The optimized lattice constants of a unit cell of the pristine BP are calculated as a = b = 3.33 Å using TS and Go6 schemes, however, the lattice constant ‘c’ is fixed at 15Å to avoid the artificial interactions between the layers. These lattice constants are closed to the previous results, i.e., a = b = 3.30 Å, a = b = 3.27 Å [26, 47-49] presented for 2D phosphorene. Furthermore, band gap results for pristine blue phosphorene have shown indirect band gap as 1.93 eV through TS scheme which is in good agreement with results reported [26]. Similar to the black phosphorene, each phosphorous atom in blue phosphorene makes three covalent bonds with its nearest neighboring atoms which reveals that three electrons in phosphorous atom becomes saturated and remaining two electrons make single lone pair, therefore, pristine blue phosphorene is non-magnetic in nature. We have investigated the doping effect on physical properties of pristine blue phosphorene by doping Ce , Ce-Ce, Ti, and Ti-Ti elements and creating single vacancy. These calculations are performed making a supercell containing 18 atoms. The optimized lattice constants of Ce, Ce-Ce, Ti, Ti-Ti doped systems and creating single vacancy in blue phosphorene are a = b = 9.85Å, a = b = 9.76 Å, a = b = 9.82 Å, a = b = 9.74 Å and 9.80Å, respectively, however, the lattice constant ‘c’ is fixed at 15Å to avoid the artificial interactions between the layers. In order to further investigate the stability of Ce, Ce-Ce, Ti
and Ti-Ti doped blue phosphorene, the binding energy of the doped systems has been calculated as follows [50]. =
/
−
−
Where EM/p, Ep and EM stands for the energy of dopant blue phosphorene, the pristine blue phosphorene and isolated dopant atoms, i.e., (Ce, Ce-Ce, Ti, Ti-Ti) respectively. ‘n’ represents the number of dopant atoms. The calculated binding energies of Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene are -10.68 eV/atom, -25.56 eV/atom, -10.79 eV/atom and 21.37 eV/atom, respectively. Comparatively, double atoms doping such as Ce-Ce, Ti-Ti doped systems seem most stable having least binding energy. It has been noticed that our calculated value of the binding energy for Ce-doped system is found to be much closer to that has already been reported by Su & Li [50] for the same system using VASP simulation code.
Figure 1: Optimized structures of (a) pristine blue phosphorene and (b) single vacancy in blue phosphorene.
Figure 2: Optimized crystal structures of (a) Ce doped and (b) Ce-Ce doped (c) Ti doped (d) Ti-Ti doped in blue phosphorene. In this section electronic properties of pristine BP, single vacancy and (Ce, Ce-Ce, Ti, Ti-Ti) doped in blue phosphorene are discussed and shown in figure 3 (a-f) wherein the band structure and density of states (DOS) are placed beside each other. The calculated indirect band gaps (as the electron-hole recombination takes place at two different k-points of the Brillouin Zone) of blue phosphorene with decreasing trend are 1.93eV (pristine), 0.35eV (with single vacancy), 0.37eV (Ce doped), 0.68eV (Ti doped) and 0.56eV (Ti-Ti doped). Whereas, for Ce-Ce doped blue phosphorene as shown in fig (3e), the system leads to metallic behavior since no band gap has been observed. The occurrence of valence band maxima and conduction band minima in Ce, Ti and Ti-Ti doped BP with respect to pristine BP are found at different symmetry points reducing the band gap energy by more than 1eV in each case. As the electrons can’t excite or radiate directly in an indirect band gap semiconductor due to different momentums of electron and hole, thus, they should undergo substantial changes in its momentum by interacting with phonons during excitation or radiation. In case of indirect band gap semiconductors, very slow radiation energy in the form of light is
emitted due to the involvement of phonons. Therefore, the blue phosphorene considered in this manuscript having indirect band gap may not be suitable for light-emitting and laser diodes fields, however, it may be applied in visible light harvesting, like the indirect band gap in phosphorene.
Figure 3: The calculated band structures and DOS of (a) pristine BP (b) with single vacancy BP (c) Ce doped (d) Ce-Ce doped (e) Ti doped and (f) Ti-Ti doped blue phosphorene. 3.2
Magnetic properties In any materials magnetism is introduced due to the combined effect of the crystal field
and constituent elements. The interstitial sites and partially filled (f/d-states) of the dopants may induce net magnetic moment [51]. Spin polarized density of states (SPDOS) with single vacancy in BP, Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene are calculated by employing DFT+U functional elongated with TS scheme as shown in figure 4(a, b). These are examined with the orbitals entailing valence electrons, i.e., P (3s2 3p3), Ce (4f1 5d1 6s2) and Ti (3d2 4s2). The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively. Whereas, the net magnetic moment for single vacancy blue phosphorene is zero. The SPDOS reveal that magnetism is induced due to the contribution of Ce and Ti atoms only while there is no significant impact of phosphorous atom. As the Ce and Ti atoms contain f and d localized energy states which may have strong correlation effect on producing magnetism. However, the use of PBE-GGA functional can’t encounter this correlation effect, i.e., on-site coulomb and on-site exchange interactions of f and d states electrons. Therefore, Hubbard Ueff parameter DFT+U has been found an appropriate remedy to address on-site self-interactions error [52] and overcome limitations of PBE-GGA. Hubbard corrections U of 6eV and 2.5eV are used for Ce and Ti atoms, respectively. As shown in figure 4 (b), Ce doped blue phosphorene exhibits semi-metallic
character [50] due to anti-symmetric behavior of spin up and spin down states, however, near the Fermi level small spin variations have been occurred due to different rate of transitions. For Ce-Ce doped system as shown figure 4 (c), the spin up and spin down states are not completely overlapped, leading to metallic behavior. Whereas, Ti doped blue phosphorene, shown in figure 4 (d), depicts semi-conducting behavior since only the spin up and spin down states in valence band are anti-symmetric, while, the spin up and down states contributing in conduction band formation have been found slightly displaced, which are not replica of each other. Moreover, few spin states have also been observed at the Fermi level, very similar to the states of band structure as displayed in figure 3(d), showing metallic behavior of the composite. In case of Ti-Ti doped system which is shown in figure 4 (e), the spin up and spin down states are not degenerated which indicates its magnetic character leading to semimetallic behavior of the system.
Figure 4: Spin polarized DOS of (a) with single vacancy (b) Ce doped (c) Ce-Ce doped (d) Ti doped (e) Ti-Ti doped in blue phosphorene.
3.3 Dynamical properties The first principles calculations of phonon frequencies are made using finite displacement method along with TS and Go6 approaches. The calculated phonon dispersion curves along high order symmetry in full Brillouin zone are shown in figures 5(a, b) to observe dynamical stability of the system. The blue phosphorene contains two atoms per unit cell, so, structure includes six branches of scattering. The phonon dispersion curves for pristine BP are depicting dynamical stability of the studied composite without any imaginary modes of phonon spectra which is in good agreement with previous results [44]. Out of six attributed modes of vibrations, three are acoustic modes and three are associated with optical modes. In lowest ZA acoustic modes, blue phosphorene is conventionally presenting wave propagation vector q2 because of bending of monolayer, while in remaining two modes (TA and LA modes) frequency has linear relation to wave vector. In both cases, the highest optical modes (LO) of vibration are found at the values ⁓ 520 cm-1. It can be seen from figure 5(a, b) that transverse optical modes (TO) have been occurred at the same frequency ⁓ 414.55cm-1 and 410.21cm-1 for TS and Go6, respectively. These optical modes were found stretching out of phase as reported earlier [44]. The highest optical modes are found splitting near the symmetry point ‘M’. The phonon band gaps are calculated as 143 cm-1 (TS) and 136 cm-1 using TS and Go6 approaches at K-point symmetry of full Brillouin Zone.
Figure 5: Calculated phonon dispersions along symmetry direction for pristine blue phosphorene using (a) TS (b) Go6 methods
3.4
Optical properties The calculation of complex dielectric function is considered one of the best approaches
to study optical properties for seeking optical response of the material at all photon energies [53]. The complex dielectric function can further be splitted into two constituent parts, i.e., real part
) and imaginary part
) =
)+
) [54] expressed as:
) 1)
The graphs of frequency dependent dielectric constants of pristine, (Ce, Ti) doped blue phosphorene plotted against photon energy range 0 – 20 eV are shown in figure 6(a-b). The real part
) of the dielectric constant is associated with dispersion and polarization of the
materials. When an electric field is applied, real part of the dielectric constant determines to what extent material has been polarized due to dipoles creation in the materials. Whereas, the imaginary part
) of the dielectric function is characterized as momentum matrix element
of occupied and unoccupied electronic states that represents absorption of incident photons falling on surface of the materials. The static values of the real dielectric constant
) are
4.13 (pristine BP), 4.83 (Ce-doped) and 4.57 (Ti-doped) which are noted zero for imaginary dielectric constant. The increasing trend of
) in lower energy range below the threshold
frequency represents the occurrence of dispersion and polarization phenomenon. However,
when incident photon’s energy meets the work function of the material,
) not only
decreases sharply to zero but extends towards negative zone representing metallic behavior of the studied compounds. As regard
), initially it is found zero at the light frequency
approximately equal to the band gap. Nevertheless, they raise their flights to gain maximum absorption peaks at 3.95 eV incident photons energy.
The absorption coefficient
) is shown in figure 6(c). It is observed that initially
absorption is zero at the light frequency equal to the band gap or below the threshold frequency. The
blue phosphorene and (Ce, Ti) doped spectra extends rapidly in the higher energy range replicating the trend as that of the imaginary part of the dielectric constant. The first peak of the absorption coefficient for the studied compounds is observed at 4.45eV with significant shift of peak of (Ce, Ti) doped towards high energy range which is clear signature of the blue shift.
2nd highest peak is observed at 8.05eV photon energy representing maximum rate of absorption. However, peaks descend gradually in further higher energy range with dispense of the absorption. The fluctuations appeared in
) might be due to the various rate of
transitions. The energy loss function versus photon energy is displayed in figure 6(d). It describes energy loss during traversal of the fast moving electrons. This quantity was defined by plasma frequency (ωp) which has been obtained at Ԑ1=0 and Ԑ2 > 1. In the present study of energy loss, the plasma frequencies are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) which fall in ultraviolet region. Beyond this energy range, the material becomes transparent because frequency of the incident photons is larger than the plasma frequency. It can also be seen from the graph that energy loss is minimal where significant absorption of the incident photons in the material surface has been observed.
Figure 6: Plot of (a) Real dielectric constant (b) Imaginary dielectric constant (b) Absorption coefficient (c) Energy Loss function for pristine, (Ce, Ti) doped blue phosphorene. 4.
CONCLUSION In the present theoretical study, we have investigated optoelectronic, magnetic and
dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP using CASTEP simulation code. The reduced band gap of Ce, Ti, Ti-Ti doped systems and single vacancy blue phosphorene exhibit that these are quite suitable for transistors and solar applications etc. The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively. Whereas, the net magnetic moment for single vacancy BP is found to be zero. The phonon dispersion curves disclosed dynamical stability of the studied pristine BP without any imaginary modes of phonon spectra with three acoustic modes and three optical modes of vibrations. The optically, plasma frequency are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) and significant shifting of absorption peak towards high energy range is clear signature of the blue shift.
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BAHAUDDIN ZAKARIYA UNIVERSITY M U L T A N DEPARTMENT OF PHYSICS Fax: + 92- 61-
Mob: +923003662924
Highlights •
Band gap is reduced by dopants (Ce, Ti, Ti-Ti) and creating single vacancy in blue phosphorene.
•
The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively but it is zero for blue phosphorene with single vacancy.
•
Pristine blue phosphorene is found to be dynamically stable without any imaginary modes of phonon spectra with three acoustic and three optical modes of vibrations.
•
Plasma frequencies are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) blue phosphorene.
BAHAUDDIN ZAKARIYA UNIVERSITY M U L T A N
DEPARTMENT OF PHYSICS Fax: +
Mob: +923003662924
CONFLICT OF INTEREST FORM Dear Editor, With reference to Ms. Ref. No.: JALCOM-D-19-15442, we are resubmitting our manuscript titled “The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study” in the Journal of Alloys and Compounds. Following the instructions of the honourable Reviewers, two doping concentrations (i.e. 5.5% and 11.0 %) of each dopant as Ce, Ce-Ce, Ti, Ti-Ti have now been investigated. Their calculated band structures along with DOS plots and spin polarized density of states have been drawn and incorporated in the revised manuscript. After thorough analysis, results of optoelectronic, magnetic and dynamical properties of (Ce, CeCe, Ti, and Ti-Ti) doped BP and with single vacancy blue phosphorene highlight their electronic band gap, magnetic and vibrational behaviour. This is an original work and not published anywhere else. All authors have proofread the manuscript and agreed to re-submit it in current form. There is no conflict of interest for all authors to publish this manuscript. Regards,
Dr. Rana M. Arif Khalil Assistant Professor Department of Physics Bahauddin Zakariya University, Multan Pakistan
Dr. Fayyaz Hussain Assistant Professor Department of Physics Bahauddin Zakariya University, Multan Pakistan
S0925-8388(20)30618-6
DOI:
https://doi.org/10.1016/j.jallcom.2020.154255
Reference:
JALCOM 154255
To appear in:
Journal of Alloys and Compounds
Received Date: 26 November 2019 Revised Date:
6 February 2020
Accepted Date: 9 February 2020
Please cite this article as: R.M.A. Khalil, F. Hussain, M.I. Hussain, A. Perveen, M. Imran, G. Murtaza, M.A. Sattar, A.M. Rana, S. Kim, The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D blue phosphorene: A dispersion corrected DFT study, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/j.jallcom.2020.154255. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
BAHAUDDIN ZAKARIYA UNIVERSITY M U L T A N
DEPARTMENT OF PHYSICS Fax: + 92- 61-
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CREDIT AUTHOR STATEMENT Dear Editor, With reference to Ms. Ref. No.: JALCOM-D-19-15442, we are resubmitting our manuscript titled “The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study”. All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in the Journal of Alloys and Compounds. Authors Contributions Conceptualization, R. M. Arif Khalil, Afshan Perveen; Methodology, Muhammad Iqbal Hussain; Software, Fayyaz Hussain; Validation, R. M. Arif Khalil, Fayyaz Hussain and Muhammad Iqbal Hussain; Formal Analysis, Afshan Perveen, Muhammad Iqbal Hussain; Investigation, Muhammad Iqbal Hussain; Resources, R. M. Arif Khalil; Data Curation, Muhammad Iqbal Hussain; WritingOriginal Draft Preparation, Muhammad Iqbal Hussain, R. M. Arif Khalil; Writing-Review & Editing, Muhammad Iqbal Hussain, R. M. Arif Khalil, Fayyaz Hussain, Muhammad Imran, Anwar Manzoor Rana, Ghulam Murtaza. M. Atif Sattar and Sungjun Kim Visualization, R. M. Arif Khalil and Muhammad Iqbal Hussain; Supervision, R. M. Arif Khalil; Project Administration, R. M. Arif Khalil; Funding Acquisition, No.
Regards,
Dr. Rana M. Arif Khalil Assistant Professor Department of Physics Bahauddin Zakariya University Multan Pakistan Dr. Fayyaz Hussain Assistant Professor Department of Physics Bahauddin Zakariya University Multan Pakistan
The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study. R. M. Arif Khalila*, Fayyaz Hussaina*, Muhammad Iqbal Hussaina,b, Afshan Perveena, Muhammad Imranc, G. Murtazad, M. A. Sattare, Anwar Manzoor Ranaa and Sungjun Kimf a Materials Simulation Research Laboratory (MSRL), Department of Physics, Bahauddin Zakariya University Multan, 60800, Pakistan b Department of Physics, University of Education, Lahore, 54000, Pakistan c Department of Physics, Govt. College University Faisalabad, Pakistan, 38000, Pakistan d Center of Advanced Studies in Physics (CASP), GC University, Lahore, 54000, Pakistan e Physics Department, College of Science, United Arab Emirates University, Al Ain, UAE f School of Electronics Engineering Chungbuk National University Cheongju 28644, South Korea
Corresponding Email*:[email protected], [email protected]
Abstract The present study has been performed to investigate optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP using the Cambridge Serial Total Energy Package (CASTEP) simulation code based on the density functional theory (DFT). The optical and vibrational properties were carried out by employing dispersion corrected density functional theory. The calculated lattice constants for pristine blue phosphorene a = b= 3.33 Å are found to be improved by Tkatchenko-Scheffler (TS) and Grimme (G06) schemes for 2D phosphorene. The band structures
and density of states results have figured out indirect band gaps as 1.93eV (pristine), 0.35eV (with single vacancy), 0.37eV (Ce doped), 0.68eV (Ti doped), and 0.56eV (Ti-Ti doped) in blue phosphorene. Whereas, no band gap has been observed for Ce-Ce doped blue phosphorene. The phonon dispersion curves obtained by density functional theory perturbation theory presented dynamical stability of the studied materials without any imaginary modes of phonon spectra. The Raman active optical modes of vibrations are found at the highest frequency of 520 cm-1. The Spin polarized density of states portray that (Ce, Ti, Ti-Ti) doped blue phosphorene exhibit semi-metallic like behavior due to hybridization of 4f, 5d and 3d localized energy states. The optical properties show that the plasma frequencies occurred at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) blue phosphorene. Moreover, significant shift of absorption peak towards high energy range is clear signature of the blue shift.
Keywords: 2D Blue Phosphorene, Dispersion correction, dynamical, phosphorene, Hubbard, spin polarized
1.
Introduction Nowadays, two dimensional (2D) materials are gaining considerable attention of
researchers due to their fascinating characteristics like electronic, optical and many others [15]. It is obvious that spin electronic appliances need identification and generation of spin electronic current, which can preferably be done using ferromagnetic semiconductors. Thus, most of the 2D materials are non-magnetic in nature [6-9]. The discovery of the graphene [10, 11], which belongs to 2D family, had open new horizons to explore and categorize numerous other 2D materials, e.g., MOS2 [12, 13] BN [14], Silicone [15], g-C3N4 [16, 17] and graphyne [18-20], etc. Besides, layered phosphorous (black phosphorene) has also been victoriously isolated through mechanical peeling from the bulk phosphorous [21-23]. It has attracted much attentions over the last few years due to its direct band gap 1.51 eV at room temperature with high mobility carriers (103 cm2 v-1 s-1) and its current on/off ratio about 104. All these magnificent features have made black phosphorene a marvelous, attractive and piquant 2D material which is a potential candidate to be utilized in optical and nano electronics tools. Tomanek et al. are pioneers who predicted blue phosphorene in 2014 as an allotrope of black phosphorene which was synthesized successfully by Zhenyu Li et al. [24, 25] from the epitaxial development on Au (111) utilizing the black phosphorene as precursor. It has honeycomb like structure similar to that of graphene. It is stable at room temperature as that of black phosphorene [26]. It has indirect band gap 2 eV [27] which makes it another optimistic allotrope of the phosphorous for its applications in nano electronic tools. Furthermore, the theoretical predictions reveal that blue phosphorene ought to be exfoliating smoothly to make quasi thin 2D patterns, which is suitable for application in nano-electronic devices [26]. To expose physical properties for the semi metallicity, Due et al. presented a model and anticipated that Fe, Co and Cr doped graphene show their behavior like semi metallic ferromagnetic [28]. Hong et al. described that substitution of Cr, Mn and Ti on black phosphorene results spin polarized semiconducting state while semi metallic state was
observed by doping either V or Fe [29]. Recently, some theoretical investigations have been made on substitutionally doping in blue phosphorene to revise its properties. Tang et al. found band gap of C and O substituted blue phosphorene [30]. They also observed that Sb and Al dopants in blue phosphorene lead transition from indirect to direct band gap. The doping Si in blue phosphorene results diluted magnetic semiconductor (DMS) like property [31]. Cho et al. explained that blue phosphorene doped with 3d transition metals such as Cr, Mn, Fe and V contaminations, Ni dopant exhibits half metallic like character whereas Sc and Co dopants display DMS and non-magnetic behavior [32]. However, up till now, no study has been done to include Van der Waals interactions in the blue phosphorene (BP). These Van der Waals interactions play crucial role to calculate the better properties of 2D BP. In the present work, dispersion corrected optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP are investigated through efficient CASTEP simulation package based on DFT. 2.
Computational Approach The first principles calculations based on density functional theory (DFT) are carried
out to investigate optoelectronic, magnetic and dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP [33, 34]. We opted norm conserving pseudo-potential [35] for these calculations. In addition, the Gaussian smearing value of 0.1 eV, cut-off energy of 540 eV along with Monkhorst–Pack [36] grid of the values 17×17×1 have been used to sample the Brillouin zone. Besides, the conjugate gradient method [37] was selected to relax the ionic positions, cell volume and lattice parameters of the system until the Hellmann Feynman forces [38] found smaller than 0.02 eV/Å and the energy convergence criteria was met at 1×10-5 eV. Perdew Burke and Ernzerhof - generalized gradient approximation (PBE-GGA) [39] has been used to describe exchange and correlation potential within the framework of CASTEP code [40]. Broyden-FletcherGoldfarb-Shannon (BFGS) method has been used for geometry optimization and achievement of optimal accuracy in results [41]. The supercell of size (3 × 3 × 1) containing
18 atoms has been taken for all configurations. Furthermore, DFT+U approach is used for magnetic calculations [42]. The vibrational behavior has been observed through finite displacement method [43, 44]. To improve the structural and vibrational properties, dispersion corrections TS [45] and G06 [46] schemes are incorporated along with exchange and correlation functional. However, the magnetic and optical calculations are performed using better dispersion corrected TS scheme. 3. 3.1
Results and Discussion Structural and electronic properties The crystal structures of pristine blue phosphorene, (Ce, Ce-Ce, Ti, Ti-Ti) doped blue
phosphorene and with singe vacancy in blue phosphorene are shown in figures (1 and 2). The optimized lattice constants of a unit cell of the pristine BP are calculated as a = b = 3.33 Å using TS and Go6 schemes, however, the lattice constant ‘c’ is fixed at 15Å to avoid the artificial interactions between the layers. These lattice constants are closed to the previous results, i.e., a = b = 3.30 Å, a = b = 3.27 Å [26, 47-49] presented for 2D phosphorene. Furthermore, band gap results for pristine blue phosphorene have shown indirect band gap as 1.93 eV through TS scheme which is in good agreement with results reported [26]. Similar to the black phosphorene, each phosphorous atom in blue phosphorene makes three covalent bonds with its nearest neighboring atoms which reveals that three electrons in phosphorous atom becomes saturated and remaining two electrons make single lone pair, therefore, pristine blue phosphorene is non-magnetic in nature. We have investigated the doping effect on physical properties of pristine blue phosphorene by doping Ce , Ce-Ce, Ti, and Ti-Ti elements and creating single vacancy. These calculations are performed making a supercell containing 18 atoms. The optimized lattice constants of Ce, Ce-Ce, Ti, Ti-Ti doped systems and creating single vacancy in blue phosphorene are a = b = 9.85Å, a = b = 9.76 Å, a = b = 9.82 Å, a = b = 9.74 Å and 9.80Å, respectively, however, the lattice constant ‘c’ is fixed at 15Å to avoid the artificial interactions between the layers. In order to further investigate the stability of Ce, Ce-Ce, Ti
and Ti-Ti doped blue phosphorene, the binding energy of the doped systems has been calculated as follows [50]. =
/
−
−
Where EM/p, Ep and EM stands for the energy of dopant blue phosphorene, the pristine blue phosphorene and isolated dopant atoms, i.e., (Ce, Ce-Ce, Ti, Ti-Ti) respectively. ‘n’ represents the number of dopant atoms. The calculated binding energies of Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene are -10.68 eV/atom, -25.56 eV/atom, -10.79 eV/atom and 21.37 eV/atom, respectively. Comparatively, double atoms doping such as Ce-Ce, Ti-Ti doped systems seem most stable having least binding energy. It has been noticed that our calculated value of the binding energy for Ce-doped system is found to be much closer to that has already been reported by Su & Li [50] for the same system using VASP simulation code.
Figure 1: Optimized structures of (a) pristine blue phosphorene and (b) single vacancy in blue phosphorene.
Figure 2: Optimized crystal structures of (a) Ce doped and (b) Ce-Ce doped (c) Ti doped (d) Ti-Ti doped in blue phosphorene. In this section electronic properties of pristine BP, single vacancy and (Ce, Ce-Ce, Ti, Ti-Ti) doped in blue phosphorene are discussed and shown in figure 3 (a-f) wherein the band structure and density of states (DOS) are placed beside each other. The calculated indirect band gaps (as the electron-hole recombination takes place at two different k-points of the Brillouin Zone) of blue phosphorene with decreasing trend are 1.93eV (pristine), 0.35eV (with single vacancy), 0.37eV (Ce doped), 0.68eV (Ti doped) and 0.56eV (Ti-Ti doped). Whereas, for Ce-Ce doped blue phosphorene as shown in fig (3e), the system leads to metallic behavior since no band gap has been observed. The occurrence of valence band maxima and conduction band minima in Ce, Ti and Ti-Ti doped BP with respect to pristine BP are found at different symmetry points reducing the band gap energy by more than 1eV in each case. As the electrons can’t excite or radiate directly in an indirect band gap semiconductor due to different momentums of electron and hole, thus, they should undergo substantial changes in its momentum by interacting with phonons during excitation or radiation. In case of indirect band gap semiconductors, very slow radiation energy in the form of light is
emitted due to the involvement of phonons. Therefore, the blue phosphorene considered in this manuscript having indirect band gap may not be suitable for light-emitting and laser diodes fields, however, it may be applied in visible light harvesting, like the indirect band gap in phosphorene.
Figure 3: The calculated band structures and DOS of (a) pristine BP (b) with single vacancy BP (c) Ce doped (d) Ce-Ce doped (e) Ti doped and (f) Ti-Ti doped blue phosphorene. 3.2
Magnetic properties In any materials magnetism is introduced due to the combined effect of the crystal field
and constituent elements. The interstitial sites and partially filled (f/d-states) of the dopants may induce net magnetic moment [51]. Spin polarized density of states (SPDOS) with single vacancy in BP, Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene are calculated by employing DFT+U functional elongated with TS scheme as shown in figure 4(a, b). These are examined with the orbitals entailing valence electrons, i.e., P (3s2 3p3), Ce (4f1 5d1 6s2) and Ti (3d2 4s2). The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively. Whereas, the net magnetic moment for single vacancy blue phosphorene is zero. The SPDOS reveal that magnetism is induced due to the contribution of Ce and Ti atoms only while there is no significant impact of phosphorous atom. As the Ce and Ti atoms contain f and d localized energy states which may have strong correlation effect on producing magnetism. However, the use of PBE-GGA functional can’t encounter this correlation effect, i.e., on-site coulomb and on-site exchange interactions of f and d states electrons. Therefore, Hubbard Ueff parameter DFT+U has been found an appropriate remedy to address on-site self-interactions error [52] and overcome limitations of PBE-GGA. Hubbard corrections U of 6eV and 2.5eV are used for Ce and Ti atoms, respectively. As shown in figure 4 (b), Ce doped blue phosphorene exhibits semi-metallic
character [50] due to anti-symmetric behavior of spin up and spin down states, however, near the Fermi level small spin variations have been occurred due to different rate of transitions. For Ce-Ce doped system as shown figure 4 (c), the spin up and spin down states are not completely overlapped, leading to metallic behavior. Whereas, Ti doped blue phosphorene, shown in figure 4 (d), depicts semi-conducting behavior since only the spin up and spin down states in valence band are anti-symmetric, while, the spin up and down states contributing in conduction band formation have been found slightly displaced, which are not replica of each other. Moreover, few spin states have also been observed at the Fermi level, very similar to the states of band structure as displayed in figure 3(d), showing metallic behavior of the composite. In case of Ti-Ti doped system which is shown in figure 4 (e), the spin up and spin down states are not degenerated which indicates its magnetic character leading to semimetallic behavior of the system.
Figure 4: Spin polarized DOS of (a) with single vacancy (b) Ce doped (c) Ce-Ce doped (d) Ti doped (e) Ti-Ti doped in blue phosphorene.
3.3 Dynamical properties The first principles calculations of phonon frequencies are made using finite displacement method along with TS and Go6 approaches. The calculated phonon dispersion curves along high order symmetry in full Brillouin zone are shown in figures 5(a, b) to observe dynamical stability of the system. The blue phosphorene contains two atoms per unit cell, so, structure includes six branches of scattering. The phonon dispersion curves for pristine BP are depicting dynamical stability of the studied composite without any imaginary modes of phonon spectra which is in good agreement with previous results [44]. Out of six attributed modes of vibrations, three are acoustic modes and three are associated with optical modes. In lowest ZA acoustic modes, blue phosphorene is conventionally presenting wave propagation vector q2 because of bending of monolayer, while in remaining two modes (TA and LA modes) frequency has linear relation to wave vector. In both cases, the highest optical modes (LO) of vibration are found at the values ⁓ 520 cm-1. It can be seen from figure 5(a, b) that transverse optical modes (TO) have been occurred at the same frequency ⁓ 414.55cm-1 and 410.21cm-1 for TS and Go6, respectively. These optical modes were found stretching out of phase as reported earlier [44]. The highest optical modes are found splitting near the symmetry point ‘M’. The phonon band gaps are calculated as 143 cm-1 (TS) and 136 cm-1 using TS and Go6 approaches at K-point symmetry of full Brillouin Zone.
Figure 5: Calculated phonon dispersions along symmetry direction for pristine blue phosphorene using (a) TS (b) Go6 methods
3.4
Optical properties The calculation of complex dielectric function is considered one of the best approaches
to study optical properties for seeking optical response of the material at all photon energies [53]. The complex dielectric function can further be splitted into two constituent parts, i.e., real part
) and imaginary part
) =
)+
) [54] expressed as:
) 1)
The graphs of frequency dependent dielectric constants of pristine, (Ce, Ti) doped blue phosphorene plotted against photon energy range 0 – 20 eV are shown in figure 6(a-b). The real part
) of the dielectric constant is associated with dispersion and polarization of the
materials. When an electric field is applied, real part of the dielectric constant determines to what extent material has been polarized due to dipoles creation in the materials. Whereas, the imaginary part
) of the dielectric function is characterized as momentum matrix element
of occupied and unoccupied electronic states that represents absorption of incident photons falling on surface of the materials. The static values of the real dielectric constant
) are
4.13 (pristine BP), 4.83 (Ce-doped) and 4.57 (Ti-doped) which are noted zero for imaginary dielectric constant. The increasing trend of
) in lower energy range below the threshold
frequency represents the occurrence of dispersion and polarization phenomenon. However,
when incident photon’s energy meets the work function of the material,
) not only
decreases sharply to zero but extends towards negative zone representing metallic behavior of the studied compounds. As regard
), initially it is found zero at the light frequency
approximately equal to the band gap. Nevertheless, they raise their flights to gain maximum absorption peaks at 3.95 eV incident photons energy.
The absorption coefficient
) is shown in figure 6(c). It is observed that initially
absorption is zero at the light frequency equal to the band gap or below the threshold frequency. The
blue phosphorene and (Ce, Ti) doped spectra extends rapidly in the higher energy range replicating the trend as that of the imaginary part of the dielectric constant. The first peak of the absorption coefficient for the studied compounds is observed at 4.45eV with significant shift of peak of (Ce, Ti) doped towards high energy range which is clear signature of the blue shift.
2nd highest peak is observed at 8.05eV photon energy representing maximum rate of absorption. However, peaks descend gradually in further higher energy range with dispense of the absorption. The fluctuations appeared in
) might be due to the various rate of
transitions. The energy loss function versus photon energy is displayed in figure 6(d). It describes energy loss during traversal of the fast moving electrons. This quantity was defined by plasma frequency (ωp) which has been obtained at Ԑ1=0 and Ԑ2 > 1. In the present study of energy loss, the plasma frequencies are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) which fall in ultraviolet region. Beyond this energy range, the material becomes transparent because frequency of the incident photons is larger than the plasma frequency. It can also be seen from the graph that energy loss is minimal where significant absorption of the incident photons in the material surface has been observed.
Figure 6: Plot of (a) Real dielectric constant (b) Imaginary dielectric constant (b) Absorption coefficient (c) Energy Loss function for pristine, (Ce, Ti) doped blue phosphorene. 4.
CONCLUSION In the present theoretical study, we have investigated optoelectronic, magnetic and
dynamical properties of pristine blue phosphorene (BP), (Ce, Ce-Ce, Ti, Ti-Ti) doped BP and single vacancy BP using CASTEP simulation code. The reduced band gap of Ce, Ti, Ti-Ti doped systems and single vacancy blue phosphorene exhibit that these are quite suitable for transistors and solar applications etc. The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively. Whereas, the net magnetic moment for single vacancy BP is found to be zero. The phonon dispersion curves disclosed dynamical stability of the studied pristine BP without any imaginary modes of phonon spectra with three acoustic modes and three optical modes of vibrations. The optically, plasma frequency are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) and significant shifting of absorption peak towards high energy range is clear signature of the blue shift.
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BAHAUDDIN ZAKARIYA UNIVERSITY M U L T A N DEPARTMENT OF PHYSICS Fax: + 92- 61-
Mob: +923003662924
Highlights •
Band gap is reduced by dopants (Ce, Ti, Ti-Ti) and creating single vacancy in blue phosphorene.
•
The net magnetic moment calculated for Ce, Ce-Ce, Ti and Ti-Ti doped blue phosphorene is 1µ B, 2µβ, 0.90 µ B and 1.80 µβ, respectively but it is zero for blue phosphorene with single vacancy.
•
Pristine blue phosphorene is found to be dynamically stable without any imaginary modes of phonon spectra with three acoustic and three optical modes of vibrations.
•
Plasma frequencies are observed at 11.34eV (pristine), 8.6 eV (Ce-doped) and 9.03eV (Ti-doped) blue phosphorene.
BAHAUDDIN ZAKARIYA UNIVERSITY M U L T A N
DEPARTMENT OF PHYSICS Fax: +
Mob: +923003662924
CONFLICT OF INTEREST FORM Dear Editor, With reference to Ms. Ref. No.: JALCOM-D-19-15442, we are resubmitting our manuscript titled “The investigation of optoelectronic, magnetic and dynamical properties of Ce and Ti doped 2D Blue Phosphorene: A Dispersion Corrected DFT study” in the Journal of Alloys and Compounds. Following the instructions of the honourable Reviewers, two doping concentrations (i.e. 5.5% and 11.0 %) of each dopant as Ce, Ce-Ce, Ti, Ti-Ti have now been investigated. Their calculated band structures along with DOS plots and spin polarized density of states have been drawn and incorporated in the revised manuscript. After thorough analysis, results of optoelectronic, magnetic and dynamical properties of (Ce, CeCe, Ti, and Ti-Ti) doped BP and with single vacancy blue phosphorene highlight their electronic band gap, magnetic and vibrational behaviour. This is an original work and not published anywhere else. All authors have proofread the manuscript and agreed to re-submit it in current form. There is no conflict of interest for all authors to publish this manuscript. Regards,
Dr. Rana M. Arif Khalil Assistant Professor Department of Physics Bahauddin Zakariya University, Multan Pakistan
Dr. Fayyaz Hussain Assistant Professor Department of Physics Bahauddin Zakariya University, Multan Pakistan