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Combined Effects of Pressure, Temperature, and Magnetic Field on the Ground State of Donor Impurities in a Gaas/Algaas Quantum Heterostructure

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Combined Effects of Pressure, Temperature, and Magnetic Field on the Ground State of Donor Impurities in a Gaas/Algaas Quantum Heterostructure Int. J. Nano Dimens., 10 (4): 375-390, Autumn 2019 ORIGINAL ARTICLE Combined effects of pressure, temperature, and magnetic field on the ground state of donor impurities in a GaAs/AlGaAs quantum heterostructure Samah Abuzaid, Ayham Shaer, Mohammad Elsaid* Department of Physics, An-Najah National University, Nablus,West Bank, Jordan Received 09 February 2019; revised 15 July 2019; accepted 20 July 2019; available online 30 July 2019 Abstract In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and magnetic field * * strength. We found that the ground state donor binding energy (BE) calculated at ωc =2 R and ω0 = 5.421R , decreases from BE=7.59822 R * to BE=2.85165 R * , as we change the impurity position from d=0.0 a* to d=0.5 a* , respectively .In addition, the combined effects of pressure and temperature on the binding energy, as a function of magnetic field strength and impurity position, had been shown using the effective-mass approximation. The numerical results show that the donor impurity binding energy enhances with increasing the pressure while it decreases as the temperature decreases. Keywords: Binding Energy; Donor Impurity; Exact Diagonalization Method; Heterostructure; Magnetic Field. How to cite this article Abuzaid S, Shaer A, Elsaid M. Combined effects of pressure, temperature, and magnetic field on the ground state of donor impurities in a GaAs/AlGaAs quantum heterostructure. Int. J. Nano Dimens., 2019; 10 (4): 375-390. INTRODUCTION Low dimensional heterostructure have been of the impurity and the coulombic interaction studied intensively in the last decades, both between the system charge carrier and the donor theoretically and experimentally [1-3]. Quantum impurity change the heterostructure energy gap confined semiconductor systems such as quantum [6, 7]. The donor impurity binding energy had well (QW), quantum well wire (QWW), quantum been investigated from bulk to the quantum dot dots (QD) and quantum rings (QR) are important where it depends on the dimensionality of the elements in the present electronic devices. The system, shape, and the impurity position [1, 8, 9]. electrical, optical and transport properties of these Also, it is affected the heterostructure properties semiconductor heterostructure systems can be by the presence of the magnetic or electrical changed by external effects like: donor impurities fields, pressure, and temperature [9, 10]. For the near the heterostructure surface, electric field, quantum dot, the donor impurity binding energy magnetic field, pressure, and temperature [3,4]. increases continuously with decreasing the dot Moreover, the effect of the donor impurity on the radius, and the applied magnetic field strength, in properties of the heterostructure materials is very addition, it depends on the impurity position [11, interesting subject which has been investigated. 12]. Adding the donor impurity atoms change the The donor binding energy had been studied effective charge and mass of it, which alter the for the quantum well by using variation method, performance of the quantum devices and the where the ground state of donor binding energy transport properties [5]. The binding energy had been computed as a function of the impurity * Corresponding Author Email: [email protected] position and the QW width under different electric This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. S. Abuzaid et al. field strengths [13, 14]. The donor impurity (CQD). Alfonso et al. in [33] had investigated the energy for the ground and excited state of two- energy states of an electron confined in a two- dimensional heterostructure had been computed dimensional (2D) plane and bound to an off- as a function of magnetic field strength, for both plane shallow donor center in the presences of weak and strong magnetic field limit, using exact an external magnetic field by using variation and and perturbation methods [15]. Chuu et al. in Ref. numerical approaches. The effect of impurity on [16] obtained the donor impurity energy levels energy levels in double quantum rings had been analytically for both donor impurity located at considered by Khajeh Salehani et al. [34]. the quantum dots center, and for donor impurity In this work, we have investigated the combined located at the axis of the quantum-well wire. Zhu effects of pressure, temperature, magnetic field and Gu in Ref. [17] investigated the dependence strength and the impurity position on the ground of the energy transition on shallow donor impurity state binding energy of the donor impurity in states in a harmonic QD by using analytical heterostructure materials. We have computed method with the presence of the magnetic field. the ground state energy level of donor impurity The energy transition changes with the magnetic in a heterostructure by solving the donor impurity field strength, where the result shows the high Hamiltonian using exact diagonalization method. effects of magnetic fields on donor impurity The Hamiltonian theory of donor impurity energy states transition [17]. The dependence of located along the growth axis under the effect of the diamagnetic susceptibility and the binding a magnetic field, pressure and temperature had energy of the donor impurity on the pressure and been presented, followed by numerical results the temperature had been shown analytically. and discussion. The conclusion is given at the end Khordad and Fathizadeh found in their recent of the work. study the diamagnetic susceptibility increases by increasing the pressure and it decreases with THEORY increasing the temperature [18]. Peter in Ref. [19] This section describes the main parts of the 2. Theory reported the binding energy levels of shallow donor impurity formulation: i) the quantum hydrogenic impurities in a parabolic quantum dot heterostructure Hamiltonian, ii) the exact This section describes the main parts of the donor impurity formulation: i) the (QD)with pressure effect using variation approach. diagonalization method and iii) the pressure and Where, they are found that the ionization energy, temperaturequantum heterostructure effects Hamiltonian, on the ii) thecomputed exact diagonalization donor method and iii) the is purely pressure-dependent. Merchancano et al. impurity ground state binding energy by the pressure and temperature effects on the computed donor impurity ground state binding in Ref. [2] had also calculated the2. Theory binding energy of effective-mass approximation. The system is a the hydrogenic impurities in a spherical QD using quantumenergy by the heterostructure effective-mass approximation. confined inThe the system x-y isplane a quantum heterostructure This section describes the main parts of the donor impurity formulation: i) the the variation and perturbation approaches as a withconfined parabolic in the x-y confinement plane with parabolic potential confinement of potential confining of confining strength quantum heterostructure Hamiltonian, ii) the exact diagonalization method and1 iii) the function of pressure, QD size, and the impurity = *ω 22 strength ω0 , Vr( ) m0 r , and in the presence 0 position. The results pressureof the and study temperature show effects that on thethe computed , donor( ) =impurity ground , and state 2 inbinding the presence of a donor impurity along the z- axis located of a donor1 ∗ 2impurity2 along the z- axis located binding energy increases with increasing the 0 energy by the effective-mass approximation. Theat system distance is2 a quantum d, under heterostructure the influence of a uniform pressure [20]. The combined effects of pressure at distance d, under the influence of a uniform magnetic field strength, B= × , confined in the x-y plane with parabolic confinementmagnetic potential of fieldconfining strength, strength B= ∇×A , applied along the and temperature on the binding energy of donor applied along the z -direction. A= ( , , 0) is the vector potential. B 0 impurity in a spherical, (QD) = with the , and presence in the presence of of a donorz -direction. impurity along A= the z (-− axisyx, located ,0) is the vector potential. 1 ∗ 2 2 2 2 − the electric field or without 2 had 0 been investigated at distance d, under the influence of a uniform magneticTheThe fieldinteraction interaction strength, B=between between× the, electron the inelectron the GaAs inlayer the and the donor impurity, [5, 21]. GaAs layer and the donor impurity, located at The exact diagonalizationapplied along themethod z -direction. had A= (been, , 0) is thelocated vector potential.at distance d along the z-direction in AlGaAs barrier, is attractive coulomb distance d along the z-direction in AlGaAs barrier, used to solve the problem of two interacting2 − isinteraction attractive energy. The coulomb Hamiltonian interaction of the donor impurity energy. can be The written in an operator electrons in the QD includingThe interaction the pressure between the andelectron in the GaAs layer and the donor impurity, Hamiltonian of the donor impurity can be written temperature effects. The magnetization and form as: located at distance d along the z-direction
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