Effect of Gaussian impurity parameters on the valence and conduction subbands and thermodynamic quantities in a doped 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 (i = e (electron), hh (heavy hole), lh (light hole)) for where ‘a’ is the wire radius and 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:where , and 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: , and [15]. The value of taken in this work is 5 nm and an energy scale () 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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