Investigation of Electronic Structure, Optical Properties, Molecular Electrostatic Potential maps (EPM) and Aquatic toxicity of HfO2, Hf0.88Si0.12O2, Hf0.88Ge0.12O2 and Hf0.88Sn0.12O2 by computational methods

This research work conveys the computationally investigation of Hafnium (IV) oxide and its doped crystals by Si, Ge and Sn atom replacing on the oxygen atom in HfO 2 . As Hafnium (IV) oxide has been used in power-electronics devices of MOSFETs and electronics as RRAM due to wide band gap which makes a vast problems creating high resistance. Regarding this case, the Hafnium (IV) oxide has selected and inputs how the band gap has reduced after doping the large surface area of atoms, such as Si, Ge and Sn. The lattice parameters and bandgaps were calculated with the Perdew-Burke-Ernzerhof (PBE), Revised Perdew-Burke-Ernzerhof (RPBE), Perdew Wang (PW91), Wu-Cohen (WC), and Perdew-BurkeErnzerhof for solids (PBEsol) non-local functionals of the generalized gradient approximations (GAA). The Perdew-Burke-Ernzerhof (PBE) functional provided better result which is similar to the reference value of mother crystal, HfO 2 . This rst principle method in view of density functional theory (DFT) focuses the structural geometry, electronic structure and optical properties employing conventional calculations pertaining to HfO 2 executing the computational tools of the CASTAP code from material studio 8.0. The band gap was recorded by 4.340 eV, 2.033 eV, 1.686 eV and 3.210 eV for HfO 2 , Hf 0.88 Si 0.12 O 2 Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 crystals through the Generalized Gradient Approximation (GGA) with Perdew Burke Ernzerhof (PBE). Secondly, it had also justied doing further investigations by GGA with RPBE, GGA with PW91, GGA with WC and GGA with PBE SOL , the band gap for HfO 2 , Hf 0.88 Si 0.12 O 2 , Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 were at 4.427 eV, 2.093 eV, 1.744 eV, and 3.262 eV, respectively using GGA with WC, 4.333 eV, 2.032 eV, 1.675 eV and 3.172 eV, respectively using GGA with PW91, 4.252 eV, 2.002 eV, 1.632eV and 3.086 eV, respectively using GGA with WC 4.245 eV, 2.001 eV, 1.629 eV, and 3.076 eV, respectively using GGA with PBE SOL . Moreover the DFT and PDOS were simulated for evaluating the nature of 6s 2 , 5p 6 , 4f 14 , 5d 2 orbital for a Hf atom, 3s 2 , 2p 6 orbital for Si atom, and 4s 2 , 3p 6 , 3d 10 orbital for Ge atom, 4d 10 , 5s 2 , 5p 2 for Sn atom and 2s and 2p orbital for O atom of Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 crystals. The optical properties, for instance, absorption, reection, refractive index, conductivity, dielectric function, loss function, electrostatic potential map and aquatic toxicity were calculated. Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 illustrates in gure It can be that function of Hf 0.88 Ge 0.12 O 2 higher than HfO 2 , Hf 0.88 Si 0.12 O 2 , and Hf 0.88 Sn 0.12 O 2 . gap has reduced and the Hf 0.88 Ge 0.12 O 2 crystal has a lower power band gap (1.686 eV) among HfO 2 , Hf 0.88 Si 0.12 O 2 , and Hf 0.88 Sn 0.12 O 2 crystals. The optical properties, due to Si, Ge and Sn doping, has changed. The optical dielectric function, absorption, reectivity, loss function, and conductivity of Hf 0.88 Si 0.12 O 2 , Hf 0.88 Ge 0.12 O 2 , and Hf 0.88 Sn 0.12 O 2 are greater than HfO 2 . Secondly, the molecular electrostatic potential maps (EPM), which explained the charge distribution of a molecule due to the properties of the nucleus and the nature of the electrostatic potential energy, has been calculated, and explain the factor of electronegativity for producing charge distribution. Moreover aquatic toxicity also investigated for HfO 2 , Hf 0.88 Si 0.12 O 2 , Hf 0.88 Ge 0.12 O 2 , and Hf 0.88 Sn 0.12 O 2 crystals. Those crystals have no aquatic toxicity, such as AMES toxicity, honey bees toxicity, rats toxicity, sh toxicity, carcinogenicity toxicity, inhibition toxicity and it could be said that these crystals are the eco-friendly materials. Finally all computational results reported that Si%, Ge% and Sn% doping in HfO 2 is almost acted as a promising eco-friendly semiconductor material for MOSFETs and RRAM whereas the Ge doping is the more ecacy.


Introduction
In the technological era, there are many challenges raised due to development of MOSFETs for ampli cation the signals or voltages in current electronics devices even future generation devices having the principle of the semiconductor [1,2]. In addition, MOSFETs consists of body, source, gate and drain, but many critical and immediate stumbling blocks are obtained during the optimization of the gate stack [3,4]. As a result, the cardinal function of MOSFETs is not working in the proper way. Speci cally, when MOSFETs is composed by HfO 2 , is able to perform the much larger memory windows even no degradation of memory [5][6][7]. The main cause is to stay a high coercive eld (1-2 MV/cm). In this case, the interfaces of HfO 2 is related with the Fermi energy level to control and amplify the electric signal or voltage from minimum conduction band (MCB) or maximum valence band (MVB) in devices, and metals body is the driving chair to operate the full procedure. Having some good user friendly properties of HfO 2 , there are some drawbacks, such as crystalline life time, wide band gap, Low-frequency noise [8], γ-ray irradiation in uence [9], lattice parameter [10], and gate dielectric function [11,12]. As a result, in the principle of interface overlapping, the Si and non-Si substrates (e.g., Ge, and Sn) are added as doping to determine their opto-electronic properties developing the useable capacity in RRAM, ferromagnetic devices [2,13], the dielectric thin lms [14], band-edge CMOS applications [15]. This manuscript has organized as follows HfO 2 , Hf 0.88 Si 0.12 O 2 Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 crystals including the electronic structure, density of states and optical properties. In this case, the GGA with PBE functional has used due to its most accuracy and acceptance for heavy metals containing crystals [16][17][18][19][20][21][22] with the comparing other ve GGA functionals.
Doping has widely been utilized and demonstrated as an effective way to improve the performance of oxide materials. Therefore, in order to improve the uniformity of the devices, a controllable resistive mechanism of the doped-oxide should be established. In this study, the in uence of Si, Ge and Sn doping on the MOSFETs, resistive random access memory (RRAM) characteristics of HfO 2 -based MOSFETs and RRAM device has been illustrated. In addition, the rst principle method has been performed to analyze the electronic structure, density of states and optical properties HfO 2 , Hf 0.88 Si 0. 12  Finally, from the perspective of our globe, especially the 3rd world countries like Bangladesh, is going to face the 4th industrial revolution in both the industries and advance electronics material sectors, where adequate MOSFETs, resistive random access memory (RRAM) characteristics of HfO 2 -based MOSFETs and RRAM device resources and development will be necessitated, otherwise, the revolutions will be hindered due to energy and lost the achievement for the goal of next development. To solve the upcoming di culties with advanced electronics material, the HfO 2 , Hf 0.88 Si 0.12 O 2 Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 crystals could be one of the promising solutions in view of scienti c evidence with commercial feasibilities.

Computational Methods
The rst principle calculations were performed by the plane-wave basis with the pseudopotential methods in the framework of DFT, as implemented in the CASTEP code [24,25]. We used ve different non-local functionals, such as generalized gradient approximations (GGA) [26]: Perdew-Burke-Ernzerhof (PBE) [27], Revised Perdew-Burke-Ernzerhof (RPBE) [28], Perdew Wang (PW91), Wu-Cohen (WC) and Perdew-Burke-Ernzerhof for solids (PBEsol). Each exchange-correlation (XC) functional was computed using two different kineticenergy cut-offs: 500 eV at norm conserving pseudo potentials, respectively. 2×2×2 Monkhorst-Pack grid was used. The self-consistent eld (SCF) tolerance was 1.0×10 −6 (eV/atom). The total energy tolerance, maximum ionic Hellmann-Feynman force, and maximum ionic displacement tolerance were 2.0×10 −6 (eV/atom), 0.006 (eV/Å) and 2.0×10 −6 (Å), respectively. For the optical spectra calculations, a dense mesh of uniformly distributed k-points is required; hence, the Brillouin zone integration was performed using a 2×4×2 grid of Monkhorst-Pack points. Next, the optical features, such as refractive index, re ectivity, absorption, conductivity and loss function, were similarly simulated for the calculation of the electronic structure and optical properties for the comparative study of band gaps for  Table 2. The minimum of conduction bands (MCB) and the maximum of valence bands (MVB) for two crystals has found in G symmetry point which have been shown in Figure 2 The band gap reduced after 12% Si, 12% Ge and 12% Sn atom doping on HfO 2 , but the direct band gap found in case of all functionals.
The crystal HfO 2 acquired indirect band gap for fear that of GGA with PBE and its value was in 4.340 eV shown in Figure 2 Secondly, it had also justi ed doing further investigations by GGA with PW91, GGA with WC, and GGA with PBEsol, the band gap for HfO 2 , Hf 0.88 Si 0.12 O 2 , Hf 0.88 Ge 0.12 O 2 and Hf 0.88 Sn 0.12 O 2 are at 4.333 eV, 2.032 eV, 1.675 eV and 3.172 eV, respectively using GGA with PW91, at 4.252 eV, 2.002 eV, 1.632eV and 3.086 eV, respectively using GGA with WC, and at 4.245 eV, 2.001 eV, 1.629 eV, and 3.076 eV, respectively using GGA with PBEsol shown in Figure 2(i) and 2(w).
The comparative study focused that the ve GGA methods provided similar results but GGA with PBE is considered as the standard method and this method provides similar reference result at 4.340 eV for mother crystal HfO 2 .

Absorption
The absorption coe cient provides useful data when these materials are used in solar energy conversion for optimal e ciency, and the absorption spectrum of a material depends on the nature of the energy band gap which follows the indirect band gap usually absorbs more temperature than the direct band gap semiconductor device, because there are fewer phonons at low temperature.

Refractive Index
The real part of refractive index indicates the amount of light refracted or curved and the imaginary or hypothetical part of refractive index indicates the mass loss coe cient and also determines the amount of emission when light travels through the materials. These optical properties like refractive index helps in quality evaluation of band gap persuaded structures for unremitting and optimal absorption of broad band spectral sources. Figure

Dielectric Function
The dielectric function is most important for semiconductor device, such as diode, MOSFETs and RRAM etc. The dielectric functions are calculated in the linear optical response system within the electric dipole approximation. The necessary momentum matrix elements are obtain by using the calculated wave functions from our pragmatic pseudo potentials. Dielectric functions that describe the materials at the nanoscale are needed, opening the way to the interpretation of experimental data and design of the composites to obtain desired optical behavior [31]. The dielectric function explains how an electric eld wills exertion with such an oscillating light wave element. The dielectric function is very necessary tool to investigate their optical properties which is related with adsorption properties as following equation for solid. ε = ε 1 (ω) + iε 2 (ω) Here, the main part or real part of the complex dielectric function ε 1 (ω) indicates the polarization and energy storage potential in the electric eld of the material due to the propagated light, while the imaginary part iε 2 (ω) represents the amount of absorption in a material, and discharging of charge storage. The probability of photon absorption for the band structure of any material is closely related to the imaginary portion of the dielectric function. A signi cant amount of imaginary dielectric function; it represents several inter-band transitions between VB and CB. From gure 7, the real portion is always higher than the imaginary part within the energy at 1.0 eV to 1.8 eV, and it must concluded that it is the energy storage materials than discharging potential materials which helps to elaborate their applications in MOSFETs and RRAM. In case of energy range from 2 eV to 4 eV the imaginary part shows higher value than real portion for HfO 2

Conductivity
A contact-free quantitative measurement sensitive to most charged reactions known as conductivity can be described in terms of band gap and electrical conduction at high (optical) frequencies[32]. Electronic conduction is nothing but putting electrons in the conduction band and by providing enough energy to an electron bound to the atoms this objective can be accomplished and can be made the electron free by breaking the bond. By shining the material with light this can easily be performed which photons do have an energy allowing the breaking of the bonds. In a solid state language, electrons can move from the valence to the conduction band by the support of photon leaving a hole in the valence band and an electrical conduction of the material will processed due to the free electron and hole. Figure 8 depicts

Loss function
There is a number of optical parameter but energy loss function is the most signi cant optical parameter which is nothing but the loss of photon energy during the reaction and which is denoted by L. During passing through the element electrons losses energy and here function L describes the impetuous energy loss of electrons. The plasma resonance and the corresponding frequency which is known as plasma frequencies are very much connected with the peaks of the L function [33]. This function has capability to cover the full energy range and has involvement in scattered elastic and non-scattered electrons and also in stimulating valence inter-band transitions or electrons in the outer shell of the atom [34].
Secondly, the loss function is a crucial part of optical properties which is composed of two regions of photon energy parts such as the lower photon energy part and higher photon energy part for crystal materials. The energy loss function is closely related to the dielectric function of the photocatalyst materials within the range of the dielectric theory validation. In the energy loss function dielectric function re ects the response of a semiconductor to an external electromagnetic perturbation.

Molecular electrostatic potential maps (EPM)
The sequence of charge distribution of a molecule due to the properties of the nucleus and the nature of the electrostatic potential energy can be revealed by the electrostatic potential map which is nothing but the charge distribution of molecules in three dimensions.
An area of higher than average electrostatic potential energy indicates the presence of a physically powerful positive charge or a weaker negative charger. The positive charge of the nucleus established the high potential energy value point to the absence of negative charge (less screening of the nucleus), which means that there are fewer electrons in this area. The discussion is true with low electrostatic potential which point outs an abundance of electrons. This feature of electrostatic potential can also be extrapolated to molecules. This property of electrostatic potentials can be extrapolated to molecules as well. In the gures 10 (a) to 10 (d), the positive electrostatic potential regions are highlighted in blue (electrophilic sites), where red represents the nucleophilic invasion region. Positively charged regions are observed to be signi cantly higher than negatively charged regions, indicating that the electrophilic groups of these molecules are more attracted to nucleophilic.

Aquatic toxicity
Aquatic toxicity is the study of the effects of chemicals and other ethnographic and natural materials and the activity on aquatic organisms that affect communities and ecosystems through individual organisms. In case of the safety of the aquatic organism, the toxicity of used materials is the crucial fact before approval to use. To create a toxicity pro le for the predicted bio-inorganic crystals, computational tools through various parameters, for example AMES toxicity, honey bees, rats and sh, carcinogenicity and inhibition have been implemented. There is no response to AMES toxicity except for all crystals. Second, there is no barrier nature by all crystals by any organism, so there is no chance of entering living cells to create damage or adverse effects for other diseases, even after entering the living cell, the carcinogenic effect is almost absent. On the other hand, Table 3 Shows that the solubility of these crystals is near to organic compounds near to -3.0 or below. The innovative feedback from these crystals is explained the effect of oxygen atoms that the solubility is changed due to change in the electronegative atoms in such a way that it does not depend on electro negativity but related to size. With increasing the size, it grows up, and similar to other parameters. Finally, it could be said that these crystals are the eco-friendly materials.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. oatimage1.jpeg