[MUSIC] Now we'll take the optical absorption, that is to say, the absorption of a photon by a semiconductor. Then we'll focus on intrinsic electrical properties of pure semiconductor without any impurity. Optical absorption can be simply this light beam. If the dI is optical absorption in a slice of thickness dx, dI is, of course, proportional to dx. The intensity be decreasing, there is minus sign. This decrease in intensity is therefore proportional to the incident intensity and multiplied by a coefficient called the absorption coefficient. Then after integration, we will obtain the relation I = I0 exponential- alpha x, where alpha is the absorption coefficient of the semiconductor, which depends on the nature of the semiconductor. Of course, part of the incident light energy can be reflected. Here, we have only treated the absorptive part of the light into the semiconductor. This optical absorption can be described as follows. You see on the left example of the valence on conduction bond in the k space. The photon absorption can be done either at the same value of the vector k, small a, and small b. This is a so called direct transition. In contrast, in case small c, the extrema of both bands differ in k value. It corresponds as an indirect transition as in silicon, for instance. The right figure displays absorption variation as function of energy of three most important crystalline semiconductor, silicon, gallium arsenide, and germanium. These three semiconductors have different band gaps. In all cases, below the gap, the material is transparent, so there is no absorption. Then above gap, the absorption is found to increase fastly. Because of its direct gap structure, the gallium arsenide absorption is totally higher than that of silicon by one or two orders of magnitude. We'll come back later on the case of germanium. Furthermore, we see that for ion energies around 3 or 4 eV, which correspond to the ultraviolet and blue light. The absorption is very high for all the semiconductors. Because it corresponds to direct transition in all the cases. In this range, high energy, photon absorption is very high, typically, 10 to the 5 or 10 to the 6 centimeters -1. This means that your light intensity decreases by about one-third, within 10 and 100 nanometers. This means that in all semiconductors, ultraviolet and blue photons are always absorbed close to the surface. Finally, the variation as function of temperature is related to thermal expansion, comparison between dashed blue and red curves. However, it is a second-order effect. We will now study the electrical properties of semiconductors on the concept of holes. More precisely, we'll investigate the consequence in terms of carrier creation of the photon absorption by a semiconductor. The mechanism of the light absorption is presented on this slide. Before the photon absorption by a semiconductor, the valence band was full and the conduction band, empty. So if an indicent photon has an energy above the band gap, it can induce a transition between the valence band, green, and the conduction band, red. This electron will be free for conduction, leaving a positive silicon ion. Then a pair of electron conduction bands vacancy in the valence band has been created. Thus, as a consequence of photon absorption, a covalent band has lost an electron in the network. Therefore, there is a positive ions since there is a lack of electron. The electron was released from the valence bands, it becomes free. This is the mechanism of the hole creation. In the presence of an electric field, the electron will drift in the opposite direction of the electric field because of the negative charge of the electron. In contrast, the electron vacancy, the so called hole, can now be filled by a nearby electron, and so on. This is equivalent to positive charge drift. So it must be understood that this is a vacancy drift without any perturbation on the silicon lattice. Thus, the presence of an electric field, the electron on the hole will drift in the opposite directions. Thus, the photon absorption has led to the creation of an electron-hole pair, the hole being an electron vacancy. We now move to the concept of the effective mass, which is discussed in detail in the next two of this chapter. In brief, we can start from the dispersion law, so the dependence of the energy on the wave vector, k. Therefore, we can develop as the vicinity of an extremum, say, the minimum of the conduction band, for example. And therefore, perform a second-order Taylor expansion. In general, the crystals are cubic, so they are symmetric. The effective mass is therefore positive and isotropic, near the minimum of the valence band. And thus, we obtain the equation E(k) = Ec, which is the energy of the minimum of the conduction band, + 2 h bar squared k squared divided by 2mc. mc is called the effective mass. So the electron near the minimum of the conduction band behaves like a free particle, but with an effective mass, which generally depart from its gravitational mass. Indeed, one can understand these phenomena physically rather simply. As the gravitational mass is created with the gravitational interaction that undergoes in a particle, the electron in the solid is not only submitted to the gravitational interaction, but to the periodical potential of the solid. Likewise, we can proceed by energy near the maximum of the valence band. Similarly, the hole behaves as a free particle, which has an effective mass, mv. In most of the semiconductor such as silicon, mv and mc are not equal. In fact, there is no physical reasons to imply that the curvature of the dispersion relation near the extrema will be the same in the valence and the conduction band. Finally, let us that the concept of effective mass is applied near the minimum and maximum of the bands respectively. These correspond to the most likely transitions, minimum in the energy difference. This is the end of the second. I remind you that the hole concept is described in the next two. In the next second, we'll address the occupation of the energy levels. Thank you. [MUSIC]