Modeling and simulation of InAs/GaAs quantum dot lasers

Abstract

Based on the analysis of carrier dynamics in quantum dots (QDs), the numerical model of InAs/GaAs QD laser is developed by means of complete rate equations. The model includes four energy levels and among them three energy levels join in lasing. A simulation is conducted by MATLAB according to the rate equation model we obtain. The simulation results of PI characteristic, gain characteristic and intensity modulation response are reasonable. Also, the relations between the left facet reflectivity of laser cavity and threshold current as well as modulation bandwidth are studied. It is indicated that the left facet reflectivity increasing can result in reduced threshold current and improved modulation bandwidth, which is in accordance with experimental results. The internal mechanism of QD lasers is fully described with the rate equation model, which is helpful for QD lasers research.It was proposed in 1982 by Y. Arakawa and H. Sakaki that reducing the dimension of the active region could significantly improve laser performance due to the quantum size effect, and they predicted the existence of quantum dots. Quantum dot is a new kind of semiconductor nanostructure that confines the movement of carriers in all three dimensions. For this reason, QDs have discrete and finite energy levels and behave like atoms, i.e., the electronic energy is quantized in three dimensions. Compared with traditional bulk laser, quantum well (QW) laser and quantum wire (QWR) laser, the QD laser uses QDs as active medium and has many advantages as follows: lower threshold current, temperature insensitivity, very small -parameter (or linewidth enhancement factor-LEF) and so on [1][2][3] . Therefore the moment QD laser has been proposed, and more and more researchers are attracted to this area.The semiconductor laser with lasing at 1.3 m becomes more and more important due to the special requirements of optical communication and data transmission technology. Among various kinds of QD lasers, the InAs/GaAs QD laser lasing at 1.3 m can be widely used in optical communication and its typical properties make it different [4][5][6][7][8][9][10] . The device prototype in this paper based on InAs/GaAs QD laser is fabricated in dots in a well (DWELL) structure. It has 10 layers of QDs. QDs facial density is 400 m -2 , active region length is 1000 m, waveguide width is 4 m, height for a single layer is 8 nm, and emission wavelength is 1.3 m, working in room temperature. Rate equation model is widely used in literature for laser modeling, which is also an effective method in QD laser modeling [5][6][7] . In this paper, according to the analysis of carrier and photon dynamic effect in active region, the QD laser numerical model is developed with complete rate equations for the first time, which includes most of key mechanisms of QDs. It is supposed that all the QDs are uniform and have exactly the same size and shape. Both homogeneous and inhomogeneous effects are ignored, and the gain spectrum is very narrow. Based on the rate equation model, MATLAB i...

Impact of Dot Size on Dynamical Characteristics of InAs/GaAs Quantum Dot Lasers

“…The required time for a process is dependent on the probability of occupation of origin and destination levels, requirements of Pauli Exclusion Principle, phonon bottleneck effect, etc. However, all these times are very short (~ps-ns) [27].…”

“…Here, 𝑁 𝛼 and 𝑆 𝛼 are respectively the carrier and photon numbers in energy level 𝛼; we consider 𝐸 𝑔 = 0.65𝑒𝑉, 𝛾 ℎ𝑜𝑚 = 10𝑚𝑒𝑉, 𝛾 0 = 20𝑚𝑒𝑉, 𝜂 𝑖 = 0.9 𝑎𝑛𝑑 Γ = 0.1 [27]. For appropriate values of the variables introduced, we refer the reader to [27,28].…”

“…Here, 𝑁 𝛼 and 𝑆 𝛼 are respectively the carrier and photon numbers in energy level 𝛼; we consider 𝐸 𝑔 = 0.65𝑒𝑉, 𝛾 ℎ𝑜𝑚 = 10𝑚𝑒𝑉, 𝛾 0 = 20𝑚𝑒𝑉, 𝜂 𝑖 = 0.9 𝑎𝑛𝑑 Γ = 0.1 [27]. For appropriate values of the variables introduced, we refer the reader to [27,28]. These seven coupled differential equations have been solved simultaneously by the forth order Runge-Kutta method to achieve the lasing behavior in time.…”

Influence of Indium-Percentage Variation on Dynamical Characteristics of InxGa1-xAs/GaAs(001) Quantum Dot Lasers

“…Each of capture, escape, relaxation or recombination with holes takes a while. The time is dependent on the probability of occupation of origin and destination levels, requirements of Pauli Exclusion Principle, phonon bottleneck effect, etc; all the times are very short (~ps-ns) [40]. By taking into account all the transitions shown in the figure, and considering the homogeneous and inhomogeneous broadening, and nonlinear gain, the rate equations can be written as follow:…”

“…Each of capture, escape, relaxation or recombination with holes takes a while. The time is dependent on the probability of occupation of origin and destination levels, requirements of Pauli Exclusion Principle, phonon bottleneck effect, etc; all the times are very short (~ps-ns) [40]. By taking into account all the transitions shown in the figure, and considering the homogeneous and inhomogeneous broadening, and nonlinear gain, the rate equations can be written as follow: (11) in which 𝑁 𝑖 and 𝑆 𝑖 respectively denote the number of carriers and photons in level i. 𝜏 𝑠𝑝 is the spontaneous recombination time, 𝜏 𝑠 is the photon lifetime into cavity [18], 𝜏 0𝑤𝑙−𝐸𝑆 2 is the initial capture time to 𝐸𝑆 2 , and 𝜏 0𝐸𝑆 2 −𝐸𝑆 1 𝑎𝑛𝑑 𝜏 0𝐸𝑆 1 −𝐺𝑆 are initial relaxation times respectively to 𝐸𝑆 2 and GS.…”