Lecture 19 Part 4 Solid StateBand Theory and

Lecture 19 Part 4: Solid State-Band Theory and Conductivity

Molecular Orbitals of Polylithium Tro: Chemistry: A Molecular Approach, 2/e 3

Band Theory • When two atomic orbitals combine they produce both a bonding and an antibonding molecular orbital • When many atomic orbitals combine they produce a band of bonding molecular orbitals and a band of antibonding molecular orbitals • The band of bonding molecular orbitals is called the valence band • The band of antibonding molecular orbitals is called the conduction band Tro: Chemistry: A Molecular Approach, 2/e 4

The band of molecular orbitals in lithium metal.

Sodium According to Band Theory Conduction band: empty 3 s antibonding No gap Valence band: full 3 s bonding 6

Magnesium 3 s bonding and antibonding should be full 7

Magnesium Conduction band: empty No gap: conductor Valence band: full Conductor 8

Copper • As the half-filled 4 s orbitals of an increasing number of Cu atoms overlap, their energies are split into a halffilled valence band. • Electrons can move from the filled half (purple) to the slightly higher energy upper half (red), where they are free to migrate from one empty orbital to another.

Solids: Conductors, Insulators and Semiconductors Conduction Band: white Band gap No gap Valence Band in red Conductor Insulator Semiconductor 10

Electrical conductivity in a conductor, semiconductor, and insulator. conductor insulator semiconductor

Band Gap • At absolute zero, all the electrons will occupy the valence band • As the temperature rises, some of the electrons may acquire enough energy to jump to the conduction band • The difference in energy between the valence band conduction band is called the band gap – the larger the band gap, the fewer electrons there are with enough energy to make the jump Tro: Chemistry: A Molecular Approach, 2/e 12

Solids: Conductors, Insulators and Semiconductors Diamond Graphite Band gap = 5. 5 e. V ≈ 530 k. J/mol No gap Conductor Insulator 13

Allotropes of Carbon • Diamond: high thermal conductivity, extremely strong, insulator • Graphite: high thermal conductivity, conductor – electrodes for electrolysis and batteries; essentially pencil “lead” 14

Diamond • Diamond has a three-dimensional network structure in which each carbon is singly-bonded to four others with sp 3 hybridization. • Diamond is a covalent network solid – each carbon covalently bonded to 4 others. • Diamonds are the hardest substance known. – must break carbon-carbon bonds • Diamonds have a melting point of 3550°C. – must break carbon-carbon bonds 15

Orbital Diagram of the sp 3 Hybridization of C 16 Tro: Chemistry: A Molecular Approach, 2/e

Methane Formation with sp 3 C 17 Tro: Chemistry: A Molecular Approach, 2/e

Structure of Diamond 18

Structure of Graphite 19

Types of Band Gaps and Conductivity Tro: Chemistry: A Molecular Approach, 2/e 20

Band Gap and Conductivity • The more electrons at any one time that a substance has in the conduction band, the better conductor of electricity it is • If the band gap is ~0, then the electrons will be almost as likely to be in the conduction band as the valence band the material will be a conductor – metals – the conductivity of a metal decreases with temperature • If the band gap is small, then a significant number of the electrons will be in the conduction band at normal temperatures and the material will be a semiconductor – graphite – the conductivity of a semiconductor increases with temperature • If the band gap is large, then effectively no electrons will be in the conduction band at normal temperatures and the material will be an insulator Tro: Chemistry: A Molecular Approach, 2/e 21

Solids: Conductors, Insulators and Semiconductors Band Gap for Semiconductors Diamond 5. 5 e. V Si 1. 1 e. V Ge 0. 67 e. V Band gap Semiconductor 22

Some semiconducting materials and associated bandgaps (e. V)

Ga. As

Doping Semiconductors • Doping is adding impurities to the semiconductor’s crystal to increase its conductivity • Goal is to increase the number of electrons in the conduction band • n-type semiconductors do not have enough electrons themselves to add to the conduction band, so they are doped by adding electron-rich impurities • p-type semiconductors are doped with an electrondeficient impurity, resulting in electron “holes” in the valence band. Electrons can jump between these holes in the valence band, allowing conduction of electricity. Tro: Chemistry: A Molecular Approach, 2/e 27

Effect of doping silicon. 28

Crystal structures and band representations of doped semiconductors.

Semiconductors • Semiconducting elements form the basis of solid state electronic devices. – When silicon is doped with phosphorus, it becomes an n-type semiconductor, in which electric current is carried by electrons. 30

Semiconductors • Semiconducting elements form the basis of solid state electronic devices. – When silicon is doped with boron, it becomes a p-type semiconductor, in which an electrical current is carried by positively charged holes 31

Diodes • When a p-type semiconductor adjoins an ntype semiconductor, the result is an p-n junction • Electricity can flow across the p-n junction in only one direction – this is called a diode • This also allows the accumulation of electrical energy – called an amplifier Tro: Chemistry: A Molecular Approach, 2/e 32

The p-n junction Forward bias Reverse bias

A p-n junction as a rectifier. 34

Light Emitting Diodes • Another important kind of diode is the light-emitting diode (LED). Whenever an electron makes a transition from the conduction band to the valence band (effectively recombining the electron and hole) there is a release of energy in the form of a photon (Figure). In some materials the energy levels are spaced so that the photon is in the visible part of the spectrum. In that case, the continuous flow of current through the LED results in a continuous stream of nearly monochromatic light. Figure: Schematic of an LED. A photon is released as an electron falls from the conduction band to the valence band. The band gap may be large enough that the photon will be in the visible portion of the spectrum. 35

Unit cell of a High Temperature Superconductor high temperature superconductor YBa 2 Cu 3 O 7

The levitating power of a superconducting oxide. rare earth magnet superconducting ceramic disk liquid nitrogen http: //www. periodictable. com/Poster. Video/Live. Action/039_Y_levitation. mov