[MUSIC] In the first step, we will describe the quantum state of the electron in a solid. This study will lead us to explain the difference between a metal, an insulator and a semiconductor as a consequence of the occupation of the band states of the crystalline solid. It is necessary to solve the Schrodinger equation in the case of a periodic potential in order to obtain the quantum states of the electron in the crystalline solid. So those were interesting to see, this detailed study should refer to the relevant annex, annex one. In summary, it appears that the dominant characteristic is the periodicity of the potential to solve the Schrodinger equation. And because of the periodicity of the potential, electron wave function has the same periodicity as the potential of the crystalline solid. The so called Bloch function extended to the bulk of the crystal. Considering the energy levels, it can be shown that the solution of the Schrodinger equation gives values of the energy E that a p has continuous function of the wave number k, p equal h bar k. You can see here a schematic typical whole presentation of possible energy values. You see that periodicity of solution base in typical conditions. In summary here, the values of the energy don't correspond to possible solutions of the Schrodinger equation. So these energy values are not possible, forbidden, hence, the notion of bandgaps. So the existence of forbidden band values appears as a consequence of the periodic potential. Moreover, we see a parabolic behaviour towards the minima here. This parabolic behaviour is reminiscence of the free box electron. And the index n is reminiscence of the quantification of the atomic levels. So in general, band structure can be represented, not necessarily in the k space, as shown here, but with density of states as function of the energy E. So now, I have shown you the possible solution. Now, we'll populate this solution with the electrons of the system while taking into account the Pauli principle. That is to say, each available state can be populated by two electrons with opposite spins at maximum. So you will see here an example of solution displaying the possible values of energy. The filling of the states by electron start from the lower energy levels, taking into account the band gap, forbidden states. You can see here two possible cases. The first one is represented in the left figure. You see that the lattice energy band called valence band is full. While on the right, the valence band is full, but some electrons begin to populate the next band called conduction band. However, the conduction band is not completely full. If the electrons completely fill one or more bands, it will be necessary to apply a very large electric field to induce a transition between the state of the valence band and the state of the conduction band. As an example, if the value of the gap is of the order of 1 electron volt, typical of silicon, the required field is at least 10 to the 9 volts per meter. So this condition will be very difficult to induce. It is clearly an insulator-like behavior without electrical conduction. On the contrary, if the last band is partly occupied, a very small amount of energy, for example, a very weak electric field, will be required to excite an electron from the last occupied state to the next one unoccupied. It means therefore that change in the energy of electron is easy to induce. So in terms of application, it means that the electron can be easily accelerated so it can be transported. This is a metal-like behavior. In summary, as [INAUDIBLE] for an insulator, the last filled band is called valence band, and the next is called conduction band. These two bands are separated by a gap. As an order of magnitude, the band gap of an insulator is typically more than 5 electron volts, a very high value as compared to kT. That is to say, the thermal excitation at room temperature, kT, is 25 milli eV. So the consequence is high resistivity, inverse of the conductivity, at ambient. So what is a semiconductor? A semiconductor is a particular case of an insulator. More precisely, it is an insulator with a band gap such that electrons can be thermally excited at the ambient with a reasonable probability. It means that the band gap is of the order of magnitude of a few electron volts, less than 5 eV. A range of resistivity is given here. The resistivity varies on almost 30 orders of magnitude from metal to insulator, which is a huge variation, semiconductor revealing an intermittent behavior. I thank you very much. I suggest to refer to the next one for more details. [MUSIC]
