A laser diode is a laser where the active region is a semiconductor. We use this device to emit photons by applying the injected electric current to it to achieve population inverse (N2>N1) and the light with a certain range of frequency to stimulate it. As we all know, only under this circumstance, the laser diode can work as a laser. Otherwise, it will work as a LED light (only spontaneous emission like figure 1).
Figure 1: spontaneous emission
When the atom spontaneously decay from a higher level to a lower level without any other stimulate, it can be defined as spontaneous emission. Spontaneous emission is the main emission pattern of LED light. Thus, if you compare a LED light (such as led streetlight, LED light) with the laser, the condensation of light of the former one is much less than the later one. That means the full width half maximum (FWHM) of the optical spectrum of LED light is larger than that of laser.
Here, we define Np as the photon density in the cavity and N as the carrier density in the cavity. The change of photon density with time can be represented as: dNp/dt; similarly, the change of electron density with time can be represented as: dN/dt; In the following steps, we will discuss the critical factor that determine dNp/dt and dN/dt.
A semiconductor has many energy levels. The band gap (Ec-Ev) of a certain semiconductor only depends on the material. Generally, an electron will stay in a lower energy level. It can convert to a higher level by absorbing energy, such as thermal energy, photons etc. It also can convert from a higher level to a lower level by emission energy (thermal or photons). There are three different conversions between electrons and photons in the cavity: spontaneous emission, stimulated emission and absorption. In the first two procedures, EHPs recombine to generate photons. While in the last procedure, a photon is absorbed to generate an EHP.