Influence of piezoelectric phonons on the magneto optical transition linewidth in GaN and GaAs

https://doi.org/10.1016/j.physe.2020.114601Get rights and content

Highlights

  • Influence of piezoelectric phonons on the magneto-optical transition linewidths (MOTLWs) in GaN and GaAs is studied.

  • MOTLWs are affected strongly by temperature, magnetic field, electron density, and well width.

  • MOTLWs for piezoelectric phonon are compared with those for optical phonon in both GaN and GaAs.

  • MOTLWs of GaN are compared with those of GaAs for both piezoelectric and optical phonons.

  • Influence of piezoelectric phonon on the MOTLWs is considerable and cannot be neglected.

Abstract

We compare piezoelectric phonon scattering mechanism with optical phonon one in both Gallium arsenide (GaAs) and Gallium nitride (GaN) materials of a quantum well through the their contribution to the magneto-optical transition linewidths (MOTLWs). Applying the projection-operator and the profile methods to compute the magneto-optical conductivity tensor (MOCT), magneto-optical absorption power (MOAP), and MOTLWs. Numerical calculation results show that the MOTLWs increase as the temperatures and the magnetic fields increase, but decrease as the electron density and the well width increase for both GaN and GaAs materials. In particular, the MOTLWs due to piezoelectric phonons vary sharper and have larger value than they do due to optical phonons in both GaN and GaAs materials, and the MOTLWs of GaN are larger than those of GaAs for both piezoelectric and optical phonon scattering mechanisms. As small enough quantum-well-width, the piezoelectric phonon modes play an important role and they should be considered in studying the magneto optical transition properties in low-dimensional electron systems.

Introduction

The investigation of the magneto-optical transition properties for low dimensional electrons systems is known to be a useful tool for studying the electronic-structure of solid, this is due to absorption linewidths are known to be very sensitive to the type of mechanisms of scattering influencing the transport-behavior of electrons in semiconductor structures [[1], [2], [3], [4], [5], [6]]. In recent years, semiconductor materials possess wide-band-gaps, for instance GaN and ZnO have attracted much interest for device applications such as the optoelectronic and electronic devices. Where GaN and ZnO have band-gaps of Eg respectively are 3.44 eV and 3.37 eV [7]. Continuing progress of GaN-material-based optoelectronic-devices for conspicuous device applications has created the significant development of the achievement of the laser diodes (LD's) and the commercialization of the high brightness green/blue lightemitting diodes (LED's) [[8], [9], [10]]. In addition to potential applications of GaN material in fabrication of optoelectronic devices, GaN is also fairly interesting from one purely physical-viewpoint. The fundamental physical natures of the GaN material can be strongly influenced and even defined by the anisotropy of the crystal quantum structures and the spatial-quantization of the states of the carrier [8]. The study of electron–phonon scattering mechanism in low-dimensional electron systems has not only practical-significance or great-importance for device applications but also important theoretical meaning in the semiconductor physics. The characteristics of quantum well systems are defined mostly through electron scattering with phonon in semiconductor physics near the room temperature. Therefore, to better understand the physical properties of electrons system in GaN and GaAs wells, the study of electron–phonon scattering mechanism is the most effective way. It is known that the type of interactions such as electron–impurity, electron–electron, and electron–phonon interactions are known to be main scattering mechanisms in low-dimensional systems. Among them electron–phonon scattering mechanism is dominant, since as low electron density as that in ordinary semiconductors, at the same time temperature of electrons system also is low then electron interaction with electron and impurity can be neglected in this case [4]. There are many types of phonon modes for interactions with electron such as piezoelectric phonon, deformation phonon, optical phonon [11], acoustic phonon [12], interface phonon [13], confine phonon [[14], [15], [16], [17]], etc. However, in this paper we are interested in the first one, and compared with the third one. The electron–piezoelectric phonon interactions occur in crystal lacking an inversion symmetry, for instance wurtzite structures or semiconductors with sphalerite. The electrons–piezoelectric phonons interactions due to a macroscopic polarization is produced from the application of an external-strain to piezoelectric material [4]. There are many theoretical approaches to study the deformation, acoustic, and optical phonon scattering mechanisms [12,[18], [19], [20], [21]] while electron–piezoelectric phonon scattering mechanism has been less interested to study in low-dimensional systems. Moreover, excellent acousto-electric properties only have in piezoelectric crystals. Therefore, such piezoelectric materials as GaN and GaAs they can be used for diverse applications such as amplifiers for ultrasonic wave, fluorescent pigments, and actinometers ect. Besides, the calculations of Jun-jie Shi [8] showed that electrophonon scatterings vigorously effected on the optical property as well as transport property of GaN semiconductors. Obviously, it is very imperative and necessary to investigate the contribution of piezoelectric phonons to electrophonon interactions in group-III nitride semiconductor structures in general and in GaN in particular. The investigation of the magneto-optical transition linewidths is known as a useful tool to examine the transport-behavior of electron system in quantum wells [[1], [2], [3], [4]]. There are many theoretical models to consider the quantum transition properties in different methodologies, among them we utilize the projection operator method because projection operators are define explicitly which can give an explicit magneto-optical transitions formula. On the other hand, the resolvent quantity contained in the MOCT being expanded with help of projection operators, and using this method we can obtaine the different Lorentzian line formula. The aim of this work is to consider the effects of piezoelectric phonons on the MOTLWs in comparison with optical phonon in both GaN and GaAs. First, we present the theory for electrons scattering mechanisms with piezoelectric and optical phonons in both GaN and GaAs materials of quantum wells. Next, we will calculate analytically the MOAP caused by piezoelectric phonon and optical phonon in both GaN and GaAs wells based on the projection operator. Finally, we show numerical calculated results for magneto-optical transition linewidth caused by the piezoelectric phonon scattering in comparison with that due to the optical phonons scattering in both GaN and GaAs by using profile method, and they are discussed in detail.

Section snippets

Scattering mechanisms of piezoelectric and optical phonons in both GaN and GaAs materials of quantum wells

We consider optical and piezoelectric phonon scattering mechanisms in GaN and GaAs wells, in the presence of magnetic field B, with confining potential V(z) for electrons system in well structure is given asV(z)=0,|z|<Lz/2,,|z|>Lz/2,the eigenfunctions Φ(r) can be written as [22]Φ(r)=1LyΨN(xx0)exp(ikyy)ψn(z),where the harmonic oscillator function and cyclotron radius respectively are symbolled by ΨN(x − x0) and ac=c/(eB), here x0=ac2ky. Moreover, we let the specimen dimension be Ly and wave

MOCT caused by the piezoelectric- and optical-phonon scatterings

Under the influence of the an electromagnetic field (EMF) where the EMF frequency ω polarized circularly in the plane (x, y), the electrons system in quantum wells structure have the MOCT is determined as [31,32]Θ±(ω)=iωlimb0+γ(jγ+)*TR{ρ(H)[Y,cγcγ+1]},here the annihilation (creation) and Liouville operators are symbolled by cγ (cγ) and L. The density operator is ρ(H), the matrix element of the current is obtained from the eigenstate as jγ+=ie2ωc(Nγ+1)/m*. The factor Y is defined by Y=(ω̄

Numerical calculations for both GaN and GaAs materials and discussions

In this Sec., we show numerical calculated results for MO-transition linewidths of cyclotron-resonance peaks caused by piezoelectric phonons scattering in comparison with that due to the optical-phonons scattering in both GaN and GaAs materials of a square potential quantum well with parameters utilized as [[34], [35], [36], [37], [38]]: m* = 0.22 × m0, ϵ0 = 8.85 × 10−12 C2/Nm2, ϵs = 9.2, ϵ = 5.35, ℏω0 = 91.8 meV, and κ = 2.6 × 10−2 m/s for GaN material; m* = 0.067m0 in which m0 is the free

Conclusions

We have studied the influence of piezoelectric phonons on the magneto-optical transition linewidths compared with optical phonons in both GaAs and GaN materials of a single quantum well. Using the projection operator we have obtained the analytical expressions for the MOCT and the MOAP of the electrons system in well. Through the numerical calculations of the analytical results, we have found the following properties of piezoelectric phonon scattering mechanism in GaN and GaAs compared with

Declaration of competing interest

We declare that we have no significant competing financial, professional, or personal interests that might have influenced the performance or presentation of the work described in this manuscript.

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