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Lecture 2 Atoms & Their Interactions

Si: the heart of electronic materials Intel, 300mm Si wafer, 200 μm thick and 48-core CPU ( cloud computing on a chip ) Twin Creeks Technologies, San Jose, Si wafer, 20 μm thick

Atomic Configuration The shell model of the atom: electrons are confined within certain shells and in subshells within shells Carbon: 1s 2 2s 2 2p 2 or [He]2s 2 2p 2 insulator, semiconductor, conductor Silicon: 1s 2 2s 2 2p 6 3s 2 3p 2 or [Ne]3s 2 3p 2 semiconductor Aluminum: [Ne]3s 2 3p 1 metal

Atomic bonding influences material properties q 1 r q 2 1. r infinity: Particles don t interact Potential energy E(r)=0 Force F=dE/dr=0

Atomic bonding influences material properties q 1 q 2 r 2. If the two particles are close enough, they will attract. This attraction is governed by electrostatic interactions: Potential energy E A (r) = -Cq 1 q 2 /r C α 1/(4πε 0 )

Atomic bonding influences material properties q 1 q 2 r 3. If the two particles are too close, they will repel. Potential energy E R (r) = +B/r m m an integer, usually large (for Na + and Cl -, m=8) For all separations, the net force exerted on the particles is the sum of attractive and repulsive forces: F=dE/dr F net =F A +F R

Force, F(r) Net Force F N =F A +F R Equilibrium E i when F N =0 r 0 =bond length

Potential energy, E(r) E R E E 0 : bond energy or cohesive energy (energy required to separate the two atoms) In general: E( r) A n r B r m E 0 E A

Types of bonds Covalent Metallic Ionic Secondary Bonding (Van der Waals) Mixed Bonding

Covalent Bonding Formation of a covalent bond between two hydrogen atoms leads to the H 2 molecule. Electrons spend majority of their time between the two nuclei which results in a net attraction between the electrons and the two nuclei.

Covalent Bonding in Methane Covalent bonding in methane, CH 4, involves four hydrogen atoms sharing bonds with one carbon atom. Each covalent bond has two shared electrons. The four bonds are identical and repel each other. In three dimensions, due to symmetry, the bonds are directed towards the corners of a tetrahedron.

Covalent Bonding in Diamond The diamond crystal is a covalently bonded network of carbon atoms Each carbon The diamond crystal is a covalently bonded network of carbon atoms. Each carbon atom is covalently bonded to four neighbors forming a regular three dimensional pattern of atoms which constitutes the diamond crystal.

Properties of covalently-bonded materials due to the strong Coulombic interaction between the shared electrons and the positive nuclei, the covalent bond energy is usually the highest among all bond types very high melting temperatures very hard solids (like diamond) insoluble in nearly all solvents Non-ductile (or non malleable) Exhibit brittle fracture under a strong force

Metallic bonding Consider Ag Electronic configuration: [Kr] 4d 10 5s 1 In metallic bonding the valence electrons from the metal atoms form a cloud of electrons which fills the space between the metal ions and glues the ions together through h the coulombic attraction between the electron gas and the positive metal ions.

Properties of metallic-bonded materials ionic cores tend to pack closely, like stacked oranges, i.e. hexagonal close-packed, face-centered centered cubic bond is non-directional under an applied force, metal ions can move with respect to each other as a result, metals are ductile electrons ect can drift freely with an applied electric ect c field high conductivity with temperature gradients, electrons can contribute to energy transfer Good thermal conductivity

Ionic bonds Bond between a positively charged ion (the cation) and a negatively charged ion (the anion) frequently found between metal atoms and non-metals i.e., NaCl Na has only one valence electron that t can be easily removed (1s 2 2s 2 2p 6 3s 1 ) Cl has 5 electrons in its 3p subshell and can readily Cl has 5 electrons in its 3p subshell, and can readily accept one more electron to close this subshell

Ionic bonds in NaCl The formation of ionic bond between Na and Cl atoms in NaCl. The attraction is due to coulombic forces.

Potential energy per ion-pair in solid NaCl Ionization energy: +1.5eV (energy to transfer the electron from Na to Cl) Cohesive energy: -6.3 ev (energy gy ( gy required to take solid NaCl apart into individual Na and Cl atoms)

A schematic illustration of a cross section from solid NaCl. NaCl is made of Cl - and Na + ions arranged alternatingly so that the oppositely charged ions are closest to each other and attract each other. There are also repulsive forces between the like ions. In equilibrium the net force acting on any ion is zero.

Properties of ionically-bonded materials Strong, brittle materials High g melting temperatures compared to metals Soluble in polar liquids No free electrons are all fairly rigidly positioned within the ions electrically insulating poor thermal conductivity

Are there bonds between atoms that have full shells, and therefore cannot share electrons? Yes! Liquid He (~4K) Solid Ar (below -189 o C) Water: although each H2O molecule is neutral, these molecules attract to form a liquid state below 100 o C and the solid state below 0 o C.

Van der Waals Forces Electrostatic attractions between the electron distribution of one atom and the positive nucleus of the other Dipole: negative and positive charge of equal magnitude Polar molecules (i.e., exhibiting a dipole) can attract or repel each other depending on their relative orientations.

Water & Van der Waals Forces The H 2 O molecule is polar and has a net permanent dipole moment Attractions between the various dipole moments in water gives rise to van der Waals bonding

Van der Waals bonding can also occur between neutral atoms based on random motions of electrons around the nucleus

Van der Waals bonding can also occur between neutral atoms based on random motions of electrons around the nucleus induced synchronization of electronic motions can lead to attractions solid Ne, Ar, liquid He also responsible for the attractive interactions between C-chains in polymers

Mixed bonding Bonding in silicon is totally covalent, because the shared electrons in the bonds are equally attracted by the neighboring positive ion cores and therefore equally shared However, where there is a covalent-type bond between different atoms, the electrons become unequally-shared GaAs, III-V compounds polar bonds i GA h l d li h l i d in GaAs, the electrons spend slightly more time around the As 5+ ion than the Ga 3+ ion

Group Activity Rank the following materials according to their melting points, from lowest to highest: NaCl Al Si He H 2 O

Group Activity Rank the following materials according to their melting points, from lowest to highest: Lowest T m (weakest bonds) Van der Waals: He (-272 o C) H-bonding: H 2 O (100 o C) metallic: Al (660 o C) ionic: NaCl (801 o C) Highest T m (strongest bonds) covalent: Si (1414 o C)

Group Activity What periodic table element do you think has the highest melting point, at ambient pressure?

Group Activity What periodic table element do you think has the highest melting point, at ambient pressure? T m =3683K (3410 o C) Note: Carbon has no melting point at atmospheric pressure, but will sublime around 4000K

Kinetic Molecular Theory Understanding the relationship between energy of atoms and temperature. Can be used to explain seemingly diverse topics as the heat capacity of metals, the average speed of electrons in a semiconductor, and electrical noise We ll start with the kinetic molecular theory of gases.