Crystalline solids. A solid crystal consists of different atoms arranged in a periodic structure.

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1 Crystalline solids A solid crystal consists of different atoms arranged in a periodic structure. Crystals can be formed via various bonding mechanisms: Ionic bonding Covalent bonding Metallic bonding Van der Waals forces /Hydrogen bonds

2 Crystalline Solids Bonding mechanisms: Ionic crystals: Example: Sodium Chloride : NaCl Each sodium ion is attracted to 6 adjacent chlorine ions, repelled by neighbouring sodium ions, attracted by other non-adjacent chlorine ions and so on. The net attractive potential per ion pair due to all the other ions in this particular geometry is U =!"k e2 r α: Madelung constant = for the NaCl crystal. All solids with the same crystal geometry have the same Madelung constant.

3 Crystalline Solids Bonding mechanisms: Ionic crystals: Example: Sodium Chloride : NaCl Each sodium ion is attracted to 6 adjacent chlorine ions, repelled by neighbouring sodium ions, attracted by other non-adjacent chlorine ions and so on. The net attractive + repulsive potential on a single sodium ion due to all the other ions in this particular geometry is U =!"k e2 r + B r m The minimum energy is the ionic cohesive energy (energy required to pull solid apart): U 0 =!"k e2 r 0 # 1! 1 & $ % m' (

4 Bonding mechanisms: Properties of Ionic crystals: Crystalline Solids Ionic cohesive energy is large, so they have high melting and boiling points. There are no free electron, so electrical conductivity is low. Can absorb infrared but not visible radiation. Easily soluble: polarized water molecule exerts a force on the ions that can break the ionic bonds. U 0 =!"k e2 r 0 # 1! 1 & $ % m' (

5 Crystalline Solids Bonding mechanisms: Covalent crystals: Example: diamond Each carbon atom in a diamond crystal is covalently bonded to four adjacent atoms in a tetrahedral lattice.

6 Bonding mechanisms: Properties of Covalent crystals: Crystalline Solids Atomic cohesive energy is larger than for ionic crystals, so covalent solids are very hard and have high melting and boiling points. Example: diamond Electrons are tightly bound, so electrical conductivity is low (good insulators). Do not absorb visible radiation.

7 Crystalline Solids Bonding mechanisms: Metallic crystals: Example: iron, copper etc Each atom loses its valence electrons to a common sea of electrons. The crystal is made of positive ion centres. Valence electrons are free to move about the positive ions in the crystal

8 Bonding mechanisms: Properties of metallic crystals: Crystalline Solids Atomic cohesive energy is smaller than for crystals, but still strong. Electrons are free to move, so electrical conductivity is high (good conductors). Can absorb and emit visible radiation close to the metal surface.

9 Band Theory of Solids Symmetric and antisymmetric wavefunctions: Two identical atoms that are far apart do not interact. Their electronic energy levels are those of individual atoms. As the atoms come closer together, the wave functions start overlapping. The joint wave functions is a symmetric or an anti-symmetric combination of the individual wave functions. Symmetric combination:! + =! 1 +! 2 Anti-symmetric combination:! " =! 1 "! 2

10 Band Theory of Solids Energy bands The energies of the symmetric and antisymmetric wavefunctions are different. So the individual atom electronic energy levels split into two. When many atoms are brought together, the energies split into more levels that are closely spaced. For N = atoms in a crystal, the energies get split into a very large number of levels, that are so closely spaced that they form an energy band. The separation between energy bands may be large or small, depending on the atom. Energy bands may overlap.

11 Band Theory of Solids Energy bands For N atoms in a crystal each energy band has N energy levels. Including the orbital angular momentum and the spin quantum numbers, each band can hold 2(2l+1)N electrons. Example: Sodium: electronic structure: 1s 2 2s 2 2p 6 3s 1 The 1s, 2s and 2p bands are full. The 3s band has one electron from each atom. Total number of electrons in the 3s band: N. The 3s band can hold 2N electrons, so it is half full.

12 Band Theory of Solids Energy bands Electrons occupying lower lying energy bands are tightly bound to the atom. The electrons in the highest energy band participate in conduction. The highest occupied energy band is called the valence band. The lowest energy band with unoccupied states is called the conduction band.

13 Band Theory of Solids Metals In metals the highest energy band is partially full. This band is both the valence band and the conduction band. There are many empty energy levels available nearby. A small electric field can excite electrons into these empty levels. Electrons are thus free to move, hence metals are good conductors.

14 Band Theory of Solids Insulators In insulators, the valence band is full. The conduction band is empty. The two bands are separated by a large energy gap. The Fermi energy lies between the gap. A small electric field cannot excite electrons from the valence to the conduction band. Hence electrons are tightly bound: the material is a good insulator.

15 Band Theory of Solids Semiconductors In semiconductors, the valence band is full at 0 temperature. The valence band and conduction band are separated by a small energy gap. The Fermi energy lies in between the gap. At non-zero temperatures, electron can cross the energy gap into the conduction band leaving holes that behave like positive charges. Conductivity of semiconductors increases with temperature. When an electric field is applied, conduction electrons move in one direction and holes move in the other direction.

16 Semiconductor Devices The band structure and conductivity of a semiconductor can be modified by adding impurities to intrinsic semiconductors. The process of adding impurities is called doping. An intrinsic semiconductor can be doped with donor atoms or acceptor atoms

17 n-type semiconductors: Semiconductor Devices Consider a semiconductor such as silicon doped with arsenic. Silicon has 4 valence electrons. Arsenic has 5 valence electrons. 4 of the arsenic electrons participate in covalent bonds with silicon atoms. The remaining arsenic electron is almost free and has an energy just below the conduction band

18 n-type semiconductors: Semiconductor Devices The arsenic donates a free electron and is called a donor atom. Semiconductors doped with donor atoms are called n-type semiconductors. A small amount of energy can raise the free electron into the conduction band. The conductivity depends on the amount of impurity.

19 p-type semiconductors: Semiconductor Devices Consider a semiconductor such as silicon doped with indium. Silicon has 4 valence electrons. Indium has 3 valence electrons. The 3 indium electrons participate in covalent bonds with silicon atoms leaving a single electron deficiency (hole). The energy of the hole lies just above the valence band. Electrons from the valence band can be excited leaving holes in the valence band.

20 p-type semiconductors: Semiconductor Devices The indium accepts an electron from the valence band and is called an acceptor atom. Semiconductors doped with acceptor atoms are called p-type. The conductivity depends on the amount of impurity.

21 Semiconductor Devices p-n junction: When an p-type semiconductor is joined to an n-type semiconductor, a p-n junction is formed. In the region around the junction, electrons move from the n-side to the p-side. In this depletion region, a net potential difference is created.

22 Diode: Semiconductor Devices When the p-n junction has a positive voltage applied to the p side (forward bias), the net voltage barrier is decreased, and hence current flow is increased. When the p-n junction has a positive voltage applied to the n side (reverse bias), the net voltage barrier is increased, and hence current flow is decreased. Thus diodes conduct in only one direction.

23 Diode: Semiconductor Devices Diodes can be used in a variety of ways such as current rectifiers, voltage regulators, switches in circuits, photomultipliers, LEDs,solar cells.

24 Transistor: A transistor consists of Semiconductor Devices an n type semiconductor between two p-type semiconductors (pnp) OR a p type semiconductor between two n type Semiconductors (npn). A small base current can control a large collector current.

25 Transistor: Semiconductor Devices Transistors, diodes, capacitors and resistors can be combined in a single integrated circuit on a silicon wafer chip. Many intergrated circuits are combined to build a computer. The low power requirements of transistors and diodes make extreme miniaturization possible without overheating. The small size allows for faster response times, increasing computational speed.