**1. Introduction**

The reduction in dimensionality caused by confining electrons (or holes) to a thin semiconductor layer leads to a dramatic change in their behavior. This principle can be developed by further reducing the dimensionality of the electron's environment from a two-dimensional quantum well to a one-dimensional quantum wire and eventually to a zero-dimensional quantum dot. In this context, however, dimensionality refers to the degree of electron momentum freedom. In fact, within a quantum wire, unlike the quantum well where the electron is confined in just one dimension, it is confined in two dimensions and thus, the freedom degree is reduced to one. In a quantum dot, the electron is confined in all three-dimensions, hence reducing the degree of freedom to zero. Under certain growth conditions, when a thin semiconductor layer grows on a substrate having a completely different lattice constant, the thin layer is spontaneously arranged or changes into quantum dots through

self-assembles while attempting to minimize the total strain energy between the bonds. Microscopy can show quantum dots that are in the shapes of pyramids, square based, and tetrahedron [1]. The performance expected from quantum dot lasers is often due to the density of their quasi-atomic states. Using the quantum structures confined in some dimensions will reduce the momentum freedom of the carrier in a certain direction. Ideally, carriers are completely enclosed in quantum dots. Therefore, the density of quantum dot states, that is, the number of states per volume unit and per energy unit, is expressed by the delta function. The gain spectrum amplitude is determined only by homogeneous broadening due to intraband relaxation at the quantum dot. These gain properties are the basis of the features that give the quantum dot laser some advantages over conventional lasers [2, 3]. The effect of carrier dynamics on the performance of quantum dot laser and the possibility of bi-exciton lasing have been studied. Bi-excitons are achieved if the increase in ground state of the quantum dot reaches the laser threshold, and if the carrier relaxation is rapidly below 100 ps, the laser will be observed [4, 5]. Carrier relaxation in quantum dots (QDs) is studied widely when applications of these devices are reported for optical communications [6]. The problem of *phonon bottlenecks* in quantum dots has sparked heated debate over whether carrier relaxation in a discrete ground state is significantly slow due to the lack of phonons required to meet the conservation rule. Because of *phonon bottleneck* [7] problem in these types of lasers, it is found that some important parameters, such as threshold current density, quantum efficiency and modulation response, are deteriorated [8]. To overcome these problems, one can manage the level spacing of a QD to decrease the carrier relaxations which inherently may decreases the laser performance, since these long relaxation times are comparable to the semiconductor radiative and non-radiative lifetimes. To have fast relaxation, overcome the phonon bottleneck problem and to improve the threshold current, external quantum efficiency, and modulation response, Auger recombination effects may be considered [9]. The most useful and well-known method to study the statics and dynamics of the carrier and photon numbers in these lasers, is to solving the rate equations for them [10]. By using the rate equations in this article and taking the Auger effect into account, a new circuit model for InGaAs-GaAs self-assembled QD (SAQD) laser will be suggested. Indeed, the Auger effect on QD laser performance are considered.
