In an ideal LED, the injected carriers are confined to the active region by the barrier layers adjoining the active regions. By means of confinement of carriers to the active region, a high carrier concentration is attained resulting in a high radiative efficiency of the recombination process. The energy barriers confining the carriers to the […]

The employment of heterostructures allows one to improve the efficiency of LEDs by confining carriers to the active region, thereby avoiding diffusion of minority carriers over long distances. Heterostructures can also be used to confine light to waveguide regions; in particular, in edge — emitting LEDs. Generally, modern semiconductor LEDs and lasers have many heterojunctions, […]

All high-intensity light-emitting diodes do not use the homojunction design but rather employ heterojunctions, which have clear advantages over homojunction devices. Heterojunction devices employ two types of semiconductors, namely a small-bandgap active region and a large-bandgap barrier region. If a structure consists of two barriers, i. e. two large-bandgap semiconductors, then the structure is called […]

The carrier distribution in p-n homojunctions, i. e. p-n junctions consisting of a single material, depends on the diffusion constant of the carriers. The diffusion constant of carriers is not easily measured. Much more common is the measurement of the carrier mobility; for example, by the Hall effect. The diffusion constant can be inferred from […]

The energy of photons emitted from a semiconductor with energy gap Eg is given by the bandgap energy, i. e. h v « Eg. (4.16) In an ideal diode, every electron injected into the active region will generate a photon. Conservation of energy thus requires that the energy with which an electron is injected is […]

The Shockley equation gives the expected theoretical I-V characteristic of a p-n junction. To describe experimentally measured characteristics, the following equation is used: I = IseV (nideal kT) (4.10) where nideal is the ideality factor of the diode. For a perfect diode, the ideality factor has a value of unity (nideal = 1.0). For real […]

2.1 Diode current—voltage characteristic The electrical characteristics of p-n junctions will be summarized, however, a detailed derivation of the results will not be provided in this chapter. We consider an abrupt p-n junction with a donor concentration of ND and an acceptor concentration of NA. All dopants are assumed to be fully ionized so that […]

The first theory of optical transitions was developed by Albert Einstein. The Einstein model includes spontaneous and stimulated or induced transitions. Spontaneous transitions occur spontaneously, that is, without an external stimulus. In contrast, stimulated transitions are induced by an external stimulus, namely a photon. Thus the induced transition rates are proportional to the photon density […]

The temperature dependence of the recombination probability is elucidated in Fig. 3.2, which shows a parabolic E(k) relationship at low and high temperatures. Inspection of the figure reveals that the number of carriers per dk interval decreases with increasing temperature. As radiative recombination requires momentum conservation and the recombination probability of an electron is proportional […]

The van Roosbroeck-Shockley model allows one to calculate the spontaneous radiative recombination rate under equilibrium and non-equilibrium conditions. To calculate the recombination rate, the model requires the knowledge of only a few basic parameters, namely the bandgap energy, the absorption coefficient, and the refractive index. All of these parameters can be determined by simple, well-known […]