[MUSIC] This course is on plastic electronics, a concept that emerged around 30 years ago. Plastic electronics combines two major technical advances of the 20th century, plastics and electronics. In the year 1907, the American Chemist Leo Baekeland, invented the first synthetic polymer, a resin called Bakelite. This was the start of plastics. Many other polymers were uncovered during the 20th century. Today, plastic are almost everywhere in our life. Right from the start, plastic were all electrical insulators. It was only in 1977 that the first electrically conducted polymer was uncovered. Its three inventors were awarded the Nobel Prize, in 2000. Now, what is electronics? The Oxford Dictionary of English defines electronics as a branch of physics and technology, concerned with the design of circuits using transistors and microchips. Commonly, electronics is perceived as a medium for the treatment and transmission of information. Most modern living would be impossible without electronics. Computers, televisions, mobile phone and satellite navigation all rely on electronics. Electronics is everywhere. Electronics emerged at the outset of the 20th century with the vacuum tube. Then came the silicon age that started with invention of the transistor in 1947, but actually developed only in the 60s. The main advantage of solid-state device over vacuum tubes are numerous, but the main one is their ability to miniaturize. This led to the tremendous development of microelectronics. But in reality vacuum tube and solid-state devices came out almost simultaneously as shown by the representative example of the diode. Here we show a patent filled by Ambrose Fleming in November 1905, that described the vacuum diode. A vacuum diode consists of two electrodes, a cathode and an anode, inside an evacuated glass bulb. The cathode is linked to a heating filament that emits electrons. When the anode is positively biased, it creates an electric field that accelerates electrons so that an electrical current passes through the device. If we reverse the bias to negative, electrons will stay around the cathode and there is no current. So the diode acts as an electrical valve. Almost together with Ambrose Flemming, the Indian Physicist Jagadish Chandra Bose and the American Engineer Greenleaf Whittier Pickard, patented the point contact diode, also known as crystal detector. The device consists of a tip that lightly touches a semiconductor crystal. At that time, the most common crystal was galena, or lead sulphide. The device also acts as a diode, in the sense that a current only flows in one direction of the electrical polarization. However, this early solid-state device was difficult to handle and much less reliable than the vacuum diode. Actually it was practically abandoned by the 1920s. The reason why solid-state electronics took so long to emerge is that it was not understood how electrons could move in a solid. A consistent explanation only came with advance of quantum mechanics in the 1930s. So what is quantum mechanics? Quantum mechanics is a branch of Physics relating to the very small. At the scale of atoms and molecules, classical mechanics ceases to be valid. Instead, the energy levels of electrons are quantized, that is, they can only occur a specific amounts. Also in classical mechanics, electrons would be in a specific place at a specific time. But in quantum mechanics, they only exist in a haze of probability. The basic equation of quantum mechanics is the time independent Schrodinger's equation. Here, H is the Hamiltonian, an operator that describes the energy of the system. Psi, is the wave function which gives the most complete description of the system. And E, is the energy of the system. In quantum mechanics, the position of a particle cannot be exactly given at all time, like in classical mechanics. Instead, one can estimate its probability density, capital P, given by the square modulus of the wave function. The Hydrogen atom is one of the rare instances when Schrodinger's equation can be exactly solved. The Hydrogen atom consists of one proton and one electron. Because the mass of the proton is much larger than that of the electron, one can assume that the proton is fixed while the electron moves, so that the Hamiltonian of the electron and the proton can be separated. This is known as the Born-Oppenheimer approximation. The Hamiltonian of the electron is the sum of its kinetic and potential energy, that is, the Coulombic attraction by the proton. The solution involves three quantum numbers that are exact integers. The principal quantum number, n, takes values equal or higher than one. The angular momentum number, l, takes value between 0 and n- 1. The magnetic number, m, can vary between -l and +l. The energy of the states only depends on the principal quantum number, n. The wave function can adopt various symmetries depending on the values of the angular momentum number. For l = 0, m can only be 0. So we have one orbital called s orbital. The orbital has a spherical symmetry, so the probability density is isotropic along all the directions of space. For l = 1, n can have three values, -1, 0, and +1. We have three orbitals, each of which can points along each of the three directions of space. These orbitals are called p orbitals. For more complex system, there is no exact solution to the Schrodinger equation. So instead solution are sought as Linear Combination of Atomic Orbitals, LCAO. An example of interest is the dihydrogen cation, which consists of two protons and one electron. The wave functions are now a combination of the atomic orbitals related to each protons. The combination can be symmetric or anti-symmetric, depending on whether it is the sum or the difference of the orbitals of each proton. In the first case, the wave function has a finite value everywhere between the two persons. In other words, the electron is shared by the two protons. Conversely the anti-symmetric orbitals falls to zero in between the two protons. This means that the presence of electron is strictly separated between the two protons. In terms of energy, we see that the energy of the atomic orbitals splits in two. The lowest level, associated with the symmetric orbital is called bonding, and the upper level, anti-bonding. Let's now turn to solids. A solid is made up of a huge number of atoms that organize themselves in crystals. In a crystal, the constituting elements, atoms or molecules, arrange according to a well-defined pattern called elemental cell, that repeats along the three direction of space. The potential energy of electrons comes from the Coulombic attraction by the protons. Now, we draw the one-dimensional potential energy of an atom, a diatomic molecule and a solid. In the latter case, the energy can be approximated to the red line, that is, a potential well. This approximation is called electron in a box. In a diatomic molecule, atomic orbitals splits in two levels. In the solid, with a great number of atoms, the atomic levels splits into this great number. So the energy difference between the sub-level is so small, that they form a quasicontinuum called energy band. Each of the atomic levels gives rise to an energy band. So the energy diagram of a solid consists of an alternation of allowed and forbidden bands. Now, we have to fill these bands with electrons. Electrons are fermions, and thus follow Pauli's principle that states that there is but one electron per state. States are filled one by one up to a given energy level called Fermi level. Mathematically speaking fermions obey Fermi-Dirac's Distribution function, which looks like a step function at zero Kelvin and slightly broadens when temperature increases. When filling the bands at zero Kelvin, two cases may occur. First, Fermi level falls within an allowed band. This band is partly filled, so the electrons at an energy close to the Fermi level have many empty sites to move to. These electrons are called free electrons because they move almost as easily as in vacuum. These solids are metals. In the second case, the Fermi level falls in a forbidden band. The band immediately below the Fermi level is completely filled, it is called valence band. The band immediately above the Fermi level is empty and is called conduction band. Electrons in a valence band cannot move because there is no empty space. While there is no electron at all in the conduction band. So electrical conduction is impossible; these solids are insulators. When temperature is raised the Fermi distribution slightly broadens. So now we can make a distinction among insulators depending on the magnitude of the energy gap. With a wide energy gap the solid still behaves as an insulator. However, when the energy gap is small the slight broadening of the Fermi distribution makes it possible to promote a small amount of electrons on top of the valence band to the bottom of the conduction band, thus making possible electrical conduction. This defines a new class of solids, the semiconductors. In summary, quantum mechanics allows for a clear distinction between metals and insulations. The metal contents a huge number of free electrons, that move almost as freely as in vacuum. The distinction between insulators and semiconductors, only intervenes at temperature above zero Kelvin. A semiconductor is an insulator with a small energy gap. Its conductivity lies between that of an insulator and that of a conductor. Importantly, this conductivity is highly changeable as will be shown all along this course. It is this unique property that make semiconductors a mandatory component in solid-state electronic devices. I thank you for your attention.
