Autoplay is onSubtitlesSettingsFull Screen2. Band structureSave noteTranscriptNotesDownloadsDiscussInteractive Transcript - Enable basic transcript mode by pressing the escape keySave NoteYou may navigate through the transcript using tab. To save a note for a section of text press CTRL + S. To expand your selection you may use CTRL + arrow key. You may contract your selection using shift + CTRL + arrow key. For screen readers that are incompatible with using arrow keys for shortcuts, you can replace them with the H J K L keys. Some screen readers may require using CTRL in conjunction with the alt keyPlay video starting at :: and follow transcript0:00[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.Play video starting at ::27 and follow transcript0:27It 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.Play video starting at :1:56 and follow transcript1:56So the existence of forbidden band values appears as a consequence of the periodic potential.Play video starting at :2:5 and follow transcript2:05Moreover, we see a parabolic behaviour towards the minima here. This parabolic behaviour is reminiscence of the free box electron.Play video starting at :2:17 and follow transcript2:17And 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.Play video starting at :2:36 and follow transcript2:36So 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.Play video starting at :3:6 and follow transcript3:06The filling of the states by electron start from the lower energy levels, taking into account the band gap, forbidden states.Play video starting at :3:17 and follow transcript3:17You 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.Play video starting at :3:30 and follow transcript3:30While 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.