We investigate exciton states theoretically in strained GaN/AlN quantum dots with wurtzite (WZ) and zinc-blende (ZB) crystal structures, as well as strained WZ GaN/AlGaN quantum dots. We show that the strain field significantly modifies the conduction and valence band edges of GaN quantum dots. The piezoelectric field is found to govern excitonic properties of WZ GaN/AlN quantum dots, while it has a smaller effect on WZ GaN/AlGaN, and very little effect on ZB GaN/AlN quantum dots. As a result, the exciton ground state energy in WZ GaN/AlN quantum dots, with heights larger than 3 nm, exhibits a red shift with respect to the bulk WZ GaN energy gap. The radiative decay time of the red-shifted transitions is large and increases almost exponentially from 6.6 ns for quantum dots with height 3 nm to 1100 ns for the quantum dots with height 4.5 nm. In WZ GaN/AlGaN quantum dots, both the radiative decay time and its increase with quantum dot height are smaller than those in WZ GaN/AlN quantum dots. On the other hand, the radiative decay time in ZB GaN/AlN quantum dots is of the order of 0.3 ns, and is almost independent of the quantum dot height. Our results are in good agreement with available experimental data and can be used to optimize GaN quantum dot parameters for proposed optoelectronic applications.

Excitonic properties of strained wurtzite and zinc-blende GaN/Al(x)Ga(1-x)N quantum dots

We investigate exciton states theoretically in strained GaN/AlN quantum dots with wurtzite (WZ) and zinc-blende (ZB) crystal structures, as well as strained WZ GaN/AlGaN quantum dots. We show that the strain field significantly modifies the conduction- and valence-band edges of GaN quantum dots. The piezoelectric field is found to govern excitonic properties of WZ GaN/AlN quantum dots, while it has a smaller effect on WZ GaN/AlGaN, and very little effect on ZB GaN/AlN quantum dots. As a result, the exciton ground state energy in WZ GaN/AlN quantum dots, with heights larger than 3 nm, exhibits a redshift with respect to the bulk WZ GaN energy gap. The radiative decay time of the redshifted transitions is large and increases almost exponentially from 6.6 ns for quantum dots with height 3 nm to 1100 ns for the quantum dots with height 4.5 nm. In WZ GaN/AlGaN quantum dots, both the radiative decay time and its increase with quantum-dot height are smaller than those in WZ GaN/AlN quantum dots. On the other hand, the radiative decay time in ZB GaN/AlN quantum dots is of the order of 0.3 ns, and is almost independent of the quantum-dot height. Our results are in good agreement with available experimental data and can be used to optimize GaN quantum-dot parameters for proposed optoelectronic applications.

Excitonic properties of strained wurtzite and zinc-blende GaN/AlxGa1−xN quantum dots

The electronic band structures of III nitride semiconductors calculated within the adiabatic approximation give essential information about the optical properties of materials. However, atoms of the lattice are not at rest; their displacement away from the equilibrium positions perturbs the periodic potential acting on the electrons in the crystal, leading to an electron-phonon interaction energy. Due to different ways that the lattice vibration perturbs the motions of electrons, there are various types of interaction, such as Frohlich interaction with longitudinal optical phonons, deformation-potential interactions with optical and acoustic phonons and piezoelectric interaction with acoustic phonons. These interactions, especially the Frohlich interaction, which is very strong due to the ionic nature of III nitrides, have a great influence on the optical properties of the III nitride semiconductors. As a result of electron-phonon interaction, several phenomena, such as phonon replicas in the emission spectra, homogeneous broadening of the excitonic line width and the relaxation of hot carriers to the fundamental band edge, which have been observed in GaN and its low dimensional heterostructures, are reviewed.

https://iopscience.iop.org/article/10.1088/0953-8984/13/32/312/pdf

Influence of electron-phonon interaction on the optical properties of III nitride semiconductors

We present an eight-band $\mathbf{k}∙\mathbf{p}$-model for the calculation of the electronic structure of wurtzite semiconductor quantum dots (QDs) and its application to indium gallium nitride $({\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N})$ QDs formed by composition fluctuations in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ layers. The eight-band $\mathbf{k}∙\mathbf{p}$-model accounts for strain effects, piezoelectricity and pyroelectricity, and spin-orbit and crystal-field splitting. Exciton binding energies are calculated using the self-consistent Hartree method. Using this model, we studied the electronic properties of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ QDs and their dependence on structural properties, i.e., their chemical composition, height, and lateral diameter. We found a dominant influence of the built-in piezoelectric and pyroelectric fields, causing a spatial separation of the bound electron and hole states and a redshift of the exciton transition energies. The single-particle energies as well as the exciton energies depend heavily on the composition and geometry of the QDs.

Interrelation of structural and electronic properties in InxGa1-xN/GaN quantum dots using an eight-band k · p model

We report the results of a variational calculation of the energy and the oscillator strength of the exciton ground state in a spherical ionic quantum dot as a function of radius, assuming infinite potential barriers. The strong interaction of the exciton with optical phonons is taken into account by using an effective potential between the electron and the hole as derived by Pollmann and B\"uttner. The values of the exciton ground-state energies calculated using this effective potential are compared with the results of a recent calculation that treats the exciton interaction with confined and interface phonons independently, and excellent agreement is found. Comparisons with two simpler models of excitons reveal that the high degree of confinement in small quantum dots suppresses polaronic corrections in exciton properties. The reduction of the electron-hole correlation in small quantum dots is observed in the behavior of oscillator strength, which becomes less dependent on the form of the effective interaction as the dot size is reduced. A proper definition of exciton transition energy in ionic materials is pointed out, where self-energy renormalization effects are important. The results of our calculation are presented for quantum dots of some ionic materials such as CdSe, GaN, ZnO, and CuCl.

Optical properties of confined polaronic excitons in spherical ionic quantum dots

Dispersion relations for polar optical phonon modes in wurtzite quantum wells (QW's) are obtained in the framework of the dielectric continuum model. It is found that anisotropy of the dielectric medium causes a number of qualitative peculiarities in the phonon spectra. Among these are the absence of the proper confinement for the oscillatory waves located in the QW, inversion of the order of symmetric and antisymmetric quasiconfined optical modes, formation of the finite energy intervals where such confined modes---which are found to be dispersive---can exist, penetration of the half-space phonons into the QW, etc. Some additional peculiarities, such as appearance of propagating modes, strong dispersion of long-wavelength half-space modes, and reduction of the number of interface modes, arise as a result of overlapping characteristic phonon frequencies of the surrounding material and the material of QW. Predicted phonon behavior leads to the conclusion that dependence of dielectric properties of ternary-binary low-dimensional wurtzite heterostructures on composition can serve as a powerful tool for the purposes of phonon spectrum engineering. In order to illustrate these results, the optical phonon spectra are calculated for an ${\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N}/\mathrm{GaN}/{\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N} \mathrm{QW},$ an $\mathrm{AlN}/\mathrm{GaN}/\mathrm{AlN} \mathrm{QW},$ and for a $\mathrm{GaN}$ dielectric slab.

Dispersion of polar optical phonons in wurtzite quantum wells

Energy-dependent electron scattering via interaction with optical phonons in wurtzite crystals and quantum wells

This paper addresses the \ifmmode \check{C}\else \v{C}\fi{}erenkov emission of high-frequency confined acoustic phonons by drifting electrons in a quantum well. We have found that the electron drift can cause strong phonon amplification (generation). The spectra of the confined modes are calculated and their confinement properties are analyzed. The spectra consist of a set of branches, and for each branch, the confinement effect increases considerably when the phonon wave vector increases. We have studied the coupling between electrons and confined modes and proved that the coupling is a nonmonotonous function of the wave vector for each of the phonon branches. We have obtained a general formula for the gain coefficient as a function of the phonon frequency and the structure parameters. For each of the branches, the amplification takes place in a spectrally separated and quite narrow amplification band in the high-frequency range. For the example of p-doped Si/SiGe/Si heterostructures it is shown that the amplification coefficients of the order of hundreds of ${\mathrm{cm}}^{\ensuremath{-}1}$ can be achieved in the sub-THz frequency range.

Generation and amplification of sub-THz coherent acoustic phonons under the drift of two-dimensional electrons

A detailed study of photoluminescence (PL) of GaN(1 nm)/Al0.2Ga0.8N(3.3 nm) twenty periods superlattice grown via metal-organic chemical vapor deposition is presented. The dependence of the PL emission energy, linewidth, and intensity on temperature, in the low temperature regime, is consistent with recombination mechanisms involving bandtail states attributed to a small degree of interfacial disorder. The activation energy of the nonradiative centers in our superlattice agrees well with the value we derive for the width of the tail-state distribution. Moreover, we find that the average phonon energy of the phonons that control the interband PL energy at high temperatures is larger for the superlattice than for a high-quality GaN film. This observation is consistent with model calculations predicting the phonon mode properties of GaN–AlN-based wurtzite heterostructures.

Photoluminescence and recombination mechanisms in GaN/Al0.2Ga0.8N superlattice

We have experimentally proven the Cerenkov generation of optical phonons by drifting electrons in a semiconductor. We observe an instability of the polar optical phonons in nanoscale semiconductors that occurs when electrons are accelerated to very high velocities by intense electric fields. The instability is observed when the electron drift velocity is larger than the phase velocity of optical phonons and rather resembles a “sonic boom” for optical phonons. The effect is demonstrated in p–i–n semiconductor nanostructures by using subpicosecond Raman spectroscopy.

/pdf/observation-of-optical-phonon-instability-induced-by-20ju1x4w0x.pdf

S. M. Komirenko

Papers

Dispersion of polar optical phonons in wurtzite quantum wells

Energy-dependent electron scattering via interaction with optical phonons in wurtzite crystals and quantum wells

Generation and amplification of sub-THz coherent acoustic phonons under the drift of two-dimensional electrons

Photoluminescence and recombination mechanisms in GaN/Al0.2Ga0.8N superlattice

Observation of optical phonon instability induced by drifting electrons in semiconductor nanostructures