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The plasma etching process plays a vital role in microelectronics chip manufacturing and cleaning of the vapour deposition reactors. Plasma etching phenomena can be better understood using plasma-chemistry models. Plasma discharge generates various gas species and gas species interact with the surface species. The interaction of gas species and surfaces species creates volatile species which can come out from the surface very easily and contributes to the surface etch. The simulation of the etching process makes the plasma etching reactor superior by enhancing the performance and exploration of processes. The simulation of the silicon etching is carried out in an NF₃ plasma reactor. The plasma chemistry along with the surface chemistry models are utilised for reaction happening inside the reactor. Reactor parameters, such as pressure, RF power deposition, mass flow rate, etc. were varied to enhance the reactor performance and understand the events’ dependency. The simulation was done using the Perrin experimental parameters and simulated results were compared with the published experimental results. The simulation is based on the mixed plasma reactor within a certain volume. It does not account for geometrical parameters and therefore it is 0-d modelling of the reactor. The simulation is based on the flow dynamics along with gas and surface chemistry. The simulation shows the same trend as the experiment. The established simulation model was also used to estimate the etch rate in future in-house experiments. The parameters and simulation results of a future in-house experiment are also included in the report. The work conducted here is to support future in-house experiments of silicon etching for better performance. This is also important for establishing an etching facility for manufacturing electronic integrated circuit and metal surface cleaning.

The D-dimensional Schrödinger equation with attractive radial potential (ARP) is solved using asymptotic iteration method, and its approximate solutions are obtained in closed form. The normalised wave function of the potential model was also determined using the hypergeometric Gauss differential equation. The variation of the energy eigenvalues of ARP with different potential parameters and quantum numbers were discussed for selected dimensions. In addition, the thermal property expressions for ARP were obtained in closed form, and their variations with temperature were discussed extensively for various values of dimension. Critical temperature values were seen to exist for specific heat capacity, at unique dimensions. Our results agree with those obtained in the literatures.

Non-Hermitian Hamiltonians respecting parity–time symmetry are well known to be associated with real spectrum, so long as (mathcal{{PT}}) symmetry is exact or unbroken, with energies turning to complex conjugate pairs as this symmetry breaks down spontaneously. Such potentials are characterised by an even real part and an odd imaginary part. However, exactly solvable quantum mechanical models are very few. In this work, we conduct an exact analytical study of a new, periodic, (mathcal{{PT}})-symmetric potential. The energies are observed to be real always, as there is no scope for spontaneous breakdown of (mathcal{{PT}}) symmetry. Using the principles of supersymmetric quantum mechanics, we find its partner Hamiltonian, sharing the same energy spectrum, with the possible exception of the ground state. Incidentally, the partner is also (mathcal{{PT}}) symmetric. Using Mathematica, we plot the exact eigenfunctions of both the partner Hamiltonians. Additionally, supersymmetric quantum mechanics (SUSY QM) helps us to find a totally new exactly solvable, non-trivial Hamiltonian, with the same energy spectrum.

Modelling biological processes is more important to analyse the real biological process in detail. Solving the modelled mathematical equations associated with the considered process/system gives us a better understanding of how complex interactions and processes work in that particular system. In this work, we consider Basener–Ross population model and study its integrability quantifiers for some restricted system parameters. We begin our analysis from finding (lambda )-symmetries. Then, we relate (lambda )-symmetries with Darboux polynomials via integrating factors. Also, we extract Lie point symmetries, null forms, Jacobi last multipliers and telescopic vector fields of the Basener–Ross population model from the obtained Darboux polynomials and (lambda )-symmetries. The obtained results will help the biologist to analyse the Basener–Ross population model in a deeper way.

This research studies the Kudryashov’s equation by using the generalised exponential rational function (GERF) technique. This technique allows us to use the traveling wave reduction for Kudryashov’s equation which provides the system of equations associated with the real and imaginary parts of the profile pulse for a complex function. First and foremost, we reduced these systems of equations into nonlinear ordinary differential equations (ODE) under the travelling wave transformations. The critical steps of the GERF technique are then applied to the resulting nonlinear ODE. With the assistance of the mentioned technique, we obtained different kinds of families of optical soliton solutions for Kudryashov’s equation. The real part, imaginary part and modulus of some of the obtained solutions are investigated/explored by the three-dimensional visual representations under the appropriate choice of the involved arbitrary parameters with suitable range space, demonstrating that the solutions represent a series of solitons, bright solitons, dark solitons, singular solitons, the interaction of solitons with solitary wave profiles, the interaction of kink waves with solitons and the interaction of kink waves with solitons.

The electronic, magnetic and thermodynamic properties of ordered and chemically disordered FeRh alloy are studied using ab-initio methods. The equiatomic Fe(_{50})Rh(_{50}) composition is reported for both ordered and disordered phases. Chemically disordered Fe(_{x})Rh(_{100-x}) is reported and the effect of disorder on electronic and magnetic properties is discussed. Further, we have reported the effects of stress and strain in both the ordered and disordered phases. The result is only for the cubic phase, and no distortion has been taken into consideration. This study is motivated by the recent resurgence in the FeRh and is inspired by the fact that it is possible to sustain the barocaloric properties over the cycle. Hence, we have discussed the properties of Fe(_{x})Rh(_{100-x}) with chemical disorder and pressure simultaneously to gain an insight into the compound effect and the interplay between them.

Because of their thermophysical and rheological properties, graphene oxide (GO) nanofluids show promising advances in heat transfer enhancement. In particular, in magnetohydrodynamic (MHD) studies, where the fluid flow is kept in check, heat transfer tends to diminish due to magnetic field strength. GO nanoparticles, with the highest thermal conductivity, significantly impacts heat transfer devices through conductive heat transfer enhancement. This paper computationally investigates the MHD flow of GO nanofluid over a linearly stretching cylinder. The nanofluid flow is modelled using Buongiorno model under the influence of viscous dissipation effects and the effects of nanoparticle characteristics such as thermophoresis and Brownian motion. The modelled equations are solved using spectral collocation method under isothermal and slip boundary conditions. An examination of the impacts of embedded parameters is presented in detail and it is shown that the conductive heat transfer and diffusive mass transfer are enhanced by dispersing GO nanoparticles in the base fluid. A quantitative analysis is made with the previously published results for special cases. As suggested, this study is significant in heat transfer applications which demand the use of magnetic fields.

In this study, electro-optical and electronic properties of 4-n-alkoxy-4(^prime )-cyanobiphenyl liquid crystal homologous series was explored. The effect of the number of carbon atoms present in the alkoxy chain on the electro-optical parameters and global reactivity descriptors has been investigated in the presence of applied electric field. Further, these parameters have also been studied under varying electric field for the homologue number, (n = 8)–12. Most of the parameters exhibit odd–even effect for a certain range of homologous numbers. The variation of the homologous number in the electric field is demonstrated to have a considerable impact on these outcomes.

We obtained the geometric phase for states of a particle in a spherical infinite potential well with moving walls in two different cases: First, when the radius of the well increases (or decreases) monotonically. Secondly, when the radius changes are oscillatory. In the latter case, we have solved the Schrödinger equation and found its solutions approximately. We obtained the transition rate for the possible real situation in an acousto-optic case which can reveal the effect of the geometric phase. We show that the absorption or radiation peaks will appear if the energy gap between the incident photon and the modified energy difference of two levels by the geometric phase is equal to the integer multiple of oscillation frequency.