As a consequence of the band gap, thermal excitation can increase the conduction band level occupation, which is initially empty in case of insulators. So, conductivity being a function of the number of carriers, as electrons in conduction band. Therefore, the conductivity increases with temperature. In contrast, the photons that have an energy smaller than the band gap, for example, the infrared photons typically less than an electron volt, will not be absorbed by the solid, because it cannot induce transition between the valence band and the conduction band. As a consequence, most semiconductors, especially those who have a band gap larger than one eV, are transparent in the infrared. On the contrary, if electrons can be excited from the valence band to the conduction band, they become free. They can be transported to the metallic electrode with the load circuit. It is a principle of the photovoltaic applications. The main semiconductor materials as the element of column IV of the periodic tables, Mendeleev's table. So, carbon, only use the diamond structure, graphite from being semi-metal, then silicone in zero below, then germanium in zero below. Then III-V compounds, from column III on V, are also semiconductors. The main materials are the gallium arsenide and indium phosphide. They're binary compounds, but it is also possible to prepare ternary on quaternary III-V alloys. II-VI semiconductors compounds are also widely used in photovoltaic application: fertile, cadmium sulfide or cadmium telluride. The semiconductor are not always monocrystallines, semiconductor can also amorphous or partially crystallines. The solid crystal can be described by your unit cell, three vectors on this unit cell isn't repeated in the solid. The results are translational symmetry in the system, in particular, for the Hamiltonian. The k-space is of major importance in semiconductor physics. The k-space is also of periodic type structure, with a unit cell repeated by transition. Because of the exponential [inaudible] of the plane wave, the real space on the k-space are conjugated spaces by Fourier transform. We will now describe the crystalline structure of silicone which is the main semiconductor used in solar photovoltaic applications. The unit cell of crystalline silicon correspond to the diamond carbon structure, namely, SP3 hybridization which will be treated later in the course. It consists of two shifted cubic lattices. This is to say that each silicon atom is bonded with four neighboring atoms, forming a tetrahedral. So, the silicon is of valence four as shown in the sphere. In the reciprocal lattice, the structure in the k-space is also a periodic array. Therefore, we'll focus on the cell that contains the origin K equals zero, the so-called first Brillouin zone. We present here the position of band structure in the k-space. Left, for silicon; on right, for gallium arsenide. So, all the curves provides a possible energy states. They are clearly bond gaps, that is to say, energy values without possible solutions of the Schrodinger equation. In the case of silicone, the minimum transition energy, that is to say, between the maximum of the valence bands and the minimum of the conductioon bands, correspond to different values of k. While in the case of gallium arsenide, it is seen that energy, this most economical transition, can be at constant value of k. So, we'll say, in the case of gallium arsenide, direct gap. On the case of silicon, indirect gap. Indeed, in silicon a change of k is required in order to induce transition between the maximum of the band valence and the minimum of the conduction band. Such an interaction in silicon will involve a phonon. Then, at higher energy, the transition can fulfill the k conservation, even in case of silicon. We'll see later the consequence of these behaviors. We present here the value of the band gap of a number of crystalline semiconductors, including silicon. This shows that the band gap of crystalline semiconductors varies from a fraction of electron volt to more than five eV for the carbon diamond. Then, it must be noticed that the most energy blue photons of the solar spectrum have an energy of the order of about three eV. As a consequence, the diamond is transparent since the most energetic solar photons cannot induce transition between the valence band on the conduction bands. Therefore, they are not useful for photovoltaic applications. However, it is shown that most of the other crystalline semiconductors may allow the absorption of solar photons. In summary, the absorption is related to a photon energy that allows a transition between valence and conduction bands. We'll treat in more details the abstraction on these consequences in the next sequence. I remind you that if you want to know in more details the quantum state of the electron in the periodic solid, I recommend you to study the Annex One. Thank you.
