Modelling of GaN quantum dot terahertz cascade laser

Abstract

In this paper GaN based spherical quantum dot cascade lasers has been modelled, where the generation of the terahertz waves are obtained. The Schrödinger, Poisson, and the laser rate equations have been solved self-consistently including all dominant physical effects such as piezoelectric and spontaneous polarization in nitride-based QDs and the effects of the temperature. The exact value of the energy levels, the wavefunctions, the lifetimes of electron levels, and the lasing frequency are calculated. Also the laser parameters such as the optical gain, the output power and the threshold current density have been calculated at different temperatures and applied electric fields.

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“…The parameters of the system are adjusted to get SPs mode energy resonant with that of the GaN QDs cascade emitter. In the particular, for a GNDs monolayer of thickness 0.34nm, Fermi energy of 0.7eV and mobility of a 10 4 cm 2 /V s with the GNDs lattice (Ag NPs lattice) embedded in a dielectric medium of dielectric constant 3 (12) with packing density 100 (150), we get SPs mode energy 41.5meV resonant with the gain medium [37]. The relaxation rates of the gain medium are set to be γ 31 = 7.14 × 10 10 s −1 , γ 32 = 7.7 × 10 10 s −1 and γ 21 = 2.2 × 10 12 s −1 [37] whereas that of SPs corresponding to E F = 0.7eV is γ sp = 7.12 × 10 11 s −1 .…”

“…In the particular, for a GNDs monolayer of thickness 0.34nm, Fermi energy of 0.7eV and mobility of a 10 4 cm 2 /V s with the GNDs lattice (Ag NPs lattice) embedded in a dielectric medium of dielectric constant 3 (12) with packing density 100 (150), we get SPs mode energy 41.5meV resonant with the gain medium [37]. The relaxation rates of the gain medium are set to be γ 31 = 7.14 × 10 10 s −1 , γ 32 = 7.7 × 10 10 s −1 and γ 21 = 2.2 × 10 12 s −1 [37] whereas that of SPs corresponding to E F = 0.7eV is γ sp = 7.12 × 10 11 s −1 . The rate of injection is set to be 10 10 s −1 and the rate of tunneling is calculated with GaN QD of dimension L QD = 4nm and effective mass of 0.2m 0 with AlGaN barrier of L b = 3nm and m b = 0.3m 0 correspondingly [45].…”

“…Moreover, GaN QDs cascade terahertz emitter, modeled for one period shown in Fig. 1, where the bold numbers denote the size of the QDs that are sandwiched between Al 0.18 Ga 0.82 N layers, have demonstrated a relatively large lifetime of the upper level leading to enhanced population inversion that supplies the spasing mode [37]. Let's first find the electric and magnetic field components of the plasmonic excitations near GNDs arrays taking into account the presence of the MNPs lattice.…”

“…22) with initial conditions; ρ 33 (0) = a * 0u (0) = 1. The penetration length of the plasmonic field is set to be equivalent to one period of the GaN QDs cascade emitter i.e., z = 17nm [37]. It can be seen that transient amplification of SPs mode of energy 41.5meV is obtained over hundreds of femtoseconds before they are damped depending on the relaxation rates of the SPs and the gain medium.…”

“…where γ out is the rate of tunneling given in terms of the dimension of QD (L QD ), and its effective mass (m QD ) as [37] :…”