Effect of Gaussian impurity parameters on the valence and conduction subbands and thermodynamic quantities in a doped quantum wire

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Highlights

  • The conduction and valence energy subband structures of a doped quantum wire with Gaussian impurity have been studied.

  • Study of the conduction and valence energy subband structures of a doped quantum wire with Gaussian impurity and the effect of impurity on the thermal quantities.

  • Numerical results show that the enhancement of decay length and strength of impurity causes the more carrier confinement and increase of energy values.

  • It is shown that the location of impurity influences on the subband structures of electrons and holes. So that, the doped quantum wire with on-center impurity has large energy eigenvalue as compared to the off-center impurity.

  • The effect of magnetic field (repulsive and attractive) on the internal energy and entropy of quantum wire has been studied.

Abstract

In this paper, the influence of impurity parameters on the energy-dispersion spectrum of electrons and holes in a doped quantum wire with Gaussian impurity is studied. The numerical calculations have shown that the energy eigenvalues enhance, if the confinement of carriers increases. Then, the energy eigenvalues rise when the magnetic field, decay length and strength of impurity increase. Also, the type of impurity affects the energy subband structures. So that, the presence of attractive impurity reduces the energy eigenvalues, as compared to repulsive impurity. Moreover, the role of impurity parameters and the external magnetic field as a control parameter on the thermal quantities has been demonstrated in details. The results show that enhancement of magnetic field, decay length and strength of repulsive impurity decreases (increases) the entropy (internal energy) of quantum wire.

Introduction

The electronic properties of semiconductors form the basis of the latest and current technological revolution, the development of ever smaller and more powerful computing devices, which affect not only the potential of modern science but also practically all aspects of our daily life. This dramatic development is based on the ability to engineer the electronic properties of semiconductors and to miniaturize devices down to the limits set by quantum mechanics. Modern crystal growth techniques make it possible to grow layers of semiconductor material, which are so small that their electronic and optical properties deviate substantially from those of bulk materials. In these structures, the energetically low-lying electron and hole states are confined in one (quantum well) or more (quantum wire (QW) or dot) directions. Quantum wires have been made in different sophisticated ways which their confinement potentials have been generated through various techniques, such as growth of structures on specially prepared substrates, using grooves, etching of quantum wells, ion implantation or with the help of induced stresses in the material below a quantum well.

One dimensional structures offer advantages for use in electronics and electro-optic devices [[1], [2], [3], [4], [5]]. Some electronic devices and bipolar transistors require both types of carriers for their operation. For this reason, interest in the physics of holes is expected to grow. Theoretical description of the top-most valance band is based upon the Luttinger model [6]. Among the articles that have utilized this model to describe holes in quantum wires can be mentioned the following: In Refs. [7], the effect of one dimensional confinement on the Zeeman splitting of hole in cylindrical quantum wires with magnetic field applied parallel to the wire axis has been investigated. But some papers have studied holes in quantum wires by a method different from the Luttinger model [8,9]. For example, confinement of electrons and holes in a heterostructured GaAs/GaP quantum wires within the effective mass approximation has been checked [8]. In this work, the confinement potential profile has been considered as Vi(ρ,z)=Qi(EgGaPEgGaAs) (i = e (electron), hh (heavy hole), lh (light hole)) for ρ<a where ‘a’ is the wire radius and Qi is the band-off-set [8,10]. In the other paper, the method is based on the coordinate transformation of V-groove quantum wire structure using a function proposed by Inoshita and then Hamiltonian has been resolved by specialized LAPACKʼs routine [9]. Moreover, energy spectra of exciton states and electron-hole complex in nanostructures has been studied in literature [[11], [12], [13], [14]]. But, it is noticeable that the valance band or holes in quantum wires are less studied than the conduction band.

Since the optical, transport and thermal properties of semiconductor materials are strongly affected by impurities in low-dimensional structures, studying the doped nanostructures becomes important. With doped semiconductor nanostructures, field has been opened for developing basic elements of semiconductor electronics, such as diodes and transistors. Only a few papers have investigated the doped quantum wire with donor impurity [15,16], as compared to the Gaussian impurity. Recently, there is an increasing interest in the research of statistical properties of quantum wires [17,18]. For example, the magnetization of low-dimensional electron systems in quantum wire arrays fabricated in modulation-doped AlGaAs/GaAs heterostructures has been investigated experimentally [17]. In other work, the effects of the Rashba spin-orbit interaction (SOI) and applied magnetic field on thermodynamic properties of a quasi-one-dimensional quantum wire at low temperatures has been studied [18]. Here, we have investigated the conduction and valance energy subbands of a doped QW with Gaussian impurity and demonstrated the effect of the impurity parameters and external fields on the band structures and thermodynamic properties in the conventional pressure.

Section snippets

Model and calculation

For modeling the confinement potential of a quantum wire, several methods have been employed [[19], [20], [21]]. Here, the wire axis and cross section have been considered in y-direction and x-z plane, respectively. Confinement potential in x (z)-direction for electrons and holes has been assumed as a harmonic oscillator (infinite well) which are given by:Vcon(x)=12mi*ω0i2x2, Vcon(z)={0,0<z<Lz, z>Lz}where mi*, ћω0i and Lz are the effective mass of carriers, strength of confinement potential of

Results and discussion

In this section, we have investigated the band structure of electrons and holes in GaAs/AlGaAs quantum wire at temperature 20 K and conventional pressure. The parameters related to material of QW are: me*=0.067 m0, γ1=6.85 and γ2=2.1 [15]. The value of Lz taken in this work is 5 nm and an energy scale (ћω0=4 meV) has been considered in our numerical calculations.

Firstly, the effect of Gaussian impurity parameters such as type of impurity, decay length, strength and position of impurity in QW on

Conclusion

In this paper, the conduction and valence energy subband structures of a doped QW with Gaussian impurity have been studied. Firstly, the effect of impurity and it's parameters on the energy subband structures has been investigated. The results show that the presence of repulsive (attractive) impurity increases (decreases) the eigenvalues of electrons and hole. Also, the enhancement of decay length and strength of impurity causes the more carrier confinement and increase of energy values. On the

Declaration of competing 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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