In the previous lecture, we have shown how quantum mechanics can explain the electrical properties of solids. We have first shown that in solids, atomic levels broaden to form an alternation of allowed and forbidden bands. By combining the energy band diagram with the Fermi distribution, we have made a distinction between metals and insulators. Finally, a distinction was made among insulators. Those with a small gap can present a small electrical conductivity at temperatures above zero Kelvin. These solids are called semiconductors. At this stage, you may ask this question. It is easy to conceive how a small numbers of electrons in the empty conduction band can lead to electrical conduction. However, how can a small number of empty states in the valence band also lead to electrical conductivity? For that imagine a one dimensional solid in which all states but one are filled. The empty state is that in light blue. Applying an electric field will make the electrons to move. They move against the direction of the field, because they bear a negative charge. So the electron next to the empty state move to the state. Now the place left by the electron is free and the next electron will move to the free state, and so on. Now let's look again at the video, but let's observe the movement of the empty state instead of that of the electrons. We see that the empty state moves along the electric field. Let's call the empty state a hole; the hole behaves like an electron, except that it bears a positive charge. Electrical current in semiconductors can be transported either by electrons or by holes. Interestingly, most of the elements of the periodic table are metals. Nonmetals occupy the upper right of the table. Many of them are actually gases or liquids. Elemental semiconductors sit at the border line between metals and nonmetals. By itself silicon is the elemental semiconductor present in more than 99% of current electronic devices. Today's lecture is to introduce organic semiconductors. Organic materials are chiefly made of carbon. So we will first speak of the carbon atom, and its ability to hybridize. Then we will show why conjugated organic molecules and polymers can be regarded as semiconductors. Organic matter refers to chemicals coming from the remains of living organisms, plants and animals. This includes coal and petroleum from which most synthetic polymers that constitute plastics are made. The chemical properties of organic matter and its derivatives mainly comes from that of its main constituent, carbon. The carbon atom has six electrons. According to quantum mechanics, atomic states can only be occupied by one electrons. Actually, because of spin degeneracy, two electrons at most can occupy a single orbital. In the first lecture, we have seen that an s state which corresponds to an angular momentum number of 0 offers one orbital, while a p state with an angular momentum of 1 generates 3 orbitals. So in the carbon atom, the 6 electrons are shared by 3 orbitals. Two electrons in the 1s state, 2 electrons in the 2s state, and the remaining two electrons in 2p states. Only the electrons with highest energy are involved in chemical reactions. So one would expect carbon to be divalent, because the states with the highest energy is a 2p state. But in reality carbon is tetravalent, this is because s and 2p orbitals hybridized to from 4 orbitals with equal energy. This hybridisation involves 1 s orbitals and 3 p orbitals, and it's called sp3. This new orbitals from sigma bonds. A representative molecule of sp3 hybridisation is methane, CH4 where the 4 hydrogens are located at the vertices of a regular tetrahedron. There are two other kinds of hybridisation. The one of interest for organic electronics is the sp2 hybridisation, when two p orbitals mix with the s orbital to form 3 sigma bonds, while the third p orbital keeps its p character, thus forming a so-called pi bond. A typical example is given by the molecule of ethylene. The three sigma bonds now points to the vertices of an equilateral triangle. The pi bond form a double bond between the two carbon atoms. We have seen in the previous lecture that the bonding of two atoms results of the splitting of the atomic energy levels into a bonding and an anti-bonding levels. Because sigma bonds are much stronger than pi bonds. The energy distance between the bonding and the anti-bonding sigma levels is much higher than for pi bonds. As a general rule the energy gap associated with sp3 orbitals is much larger than with sp2 orbitals. Most plastics are made of aliphatic polymers, only linked by sigma bonds. These solids are electrically insulating, because their energy gap is large. By contrast, conjugated molecule and polymers have narrow energy gaps, and are then expected to behave as semiconductors. Another molecule of interest is benzene C6H6, which consists of six sp2 carbon atoms forming a plane hexagon. The six pi electrons are delocalized over the entire ring. In Benzene there are 18 sigma bonds and 6 pi bonds. The six degenerate bonding and anti-bonding pi orbitals from the starting point of energy bands, the so called frontiers orbitals. The concept of frontier orbital was first introduced by the Japanese chemist, Kenichi Fukui. It states that the orbitals of importance for establishing the chemical reactivity of molecules are those located close to the Fermi level. The highest occupied molecular orbital or HOMO is the orbital just below the Fermi level. The lowest unoccupied molecular orbital or LUMO is located just above the Fermi level. By extension HOMO and LUMO levels are often used in place of valence and conjunction bonds in organic semiconductors. Conjugated polymers and small molecules form the vast family of organic semiconductors. sp2 carbon induce an alternation of single and double bonds and a small HOMO-LUMO gap. Conjugated polymers were once called conducting polymers, because of their ability to become conductive when chemically or electrochemically doped. The first one was polyacetylene, the invention of which led MacDiarmid, Shirakawa, and Heeger to the Nobel Prize. However, polyacetylene is highly sensitive to oxygen, and now other more stable polymers like polyphenylene and polythiophene are preferred. Poly-phenylene-vinylene is a combination between polyacetylene and polyphenylene. Conjugated small molecules includes oligomers of the same families of the conjugated polymers like oligothiopenes. They also comprise condensed molecules like polyacenes, made of two to five condensed Benzene rings. More recently, researchers have introduced molecules that mix Benzene and thiophene rings, like in the case of DNTT. In summary, the chemical and physical properties of organic matter is mainly dictated by that of its chief constituent, carbon. Carbon atom is tetravalent, a property due to the hybridization of its orbitals. sp3 hybridization leads to a strong sigma bonds and large HOMO-LUMO gaps. Most plastics are electrical insulators, because they are made of aliphatic chains. SP2 hybridization gives rise to weak pi bonds and reduced HOMO-LUMO gaps. For this reason, conjugated polymers and small molecules behave as semiconductors. During the next lecture we will see that organic and inorganic semiconductors present many differences. This table displays some of them. A fundamental one is the binding energy. Inorganic solids are made of atoms that are strongly linked together via covalent or ionic bonds. Organic solids are formed of molecules and although chemical bonds within each molecule are strong, these molecules are only weakly linked together. A primary consequence is that their mechanical resistance is much weaker than that of inorganic solids. We will see that it has also strong influence on their electrical and optical properties. I thank you for your attention.
