EEE 3394 Electronic Materials Chris Ferekides SPRING 2014 WEEK 2

DEFECTS What are defects? 1.POINT DEFECTS: Vacancy Interstitial Substitutional

DEFECTS What are defects? 2.Schottky Defect 3.Frenkel Defect 4.LINE DEFECTS Edge dislocation Screw dislocation A C D Dislocation line

DEFECTS What are defects? 5.Planar Defects Grain boundaries

Crystal Structure ???

Kinetic Molecular Theory What is it? What do we need it for? Links the “macroscopic” properties of gases and solids to the kinetic energy of atoms/molecules; Explains the pressure of gases … heat capacity of metals … average speed of electrons in semiconductors etc. Assumes that atoms/molecules of gases, liquids, solids are in constant motion when above absolute zero temperature KMT of gases … from Newton’s 2 nd Law …dp/dt=Force Empirical Result See assumptions in text …...molecules in constant motion.. collision time negligible compared to free motion.. collisions are elastic.. no effect from external forces etc.

Consider N molecules inside a cubic volume of side a The change in momentum of a molecule that collides with one of the walls is … Force exerted by gas on a wall is equal to the rate of change in momentum … The total pressure is equal to the total force per unit area … Due to random motion and collisions, mean square velocity in x direction same as in y and z directions … average velocity is 1/3 of v x Derivation

Compare … …where k is Boltzman’s constant Therefore … the mean square velocity is proportional to T! … adding heat to a gas … raises its temperature and total internal energy! Rise in internal energy per unit temperature – HEAT CAPACITY Derivation

Heat Capacity... Energy (U) increase per unit temperature (T) Molar Heat Capacity C m : heat capacity of one mole … for a monatomic gas … above based on constant volume … because all added energy is considered to contribute to the temperature rise and not volume expansion (i.e. doing work to increase volume)

Maxwell’s Principle of Equipartition of Energy... assigns 1/2kT to each “independent way” (degrees of freedom) a molecule can absorb energy For example: 3 degrees of freedom … 5 degrees of freedom … Degrees of Freedom: Monatomic gas – 3 translational… Diatomic gas – 5 … rotational Solid – 6 … 3 kinetic energy of vibration… + 3 potential energy of “spring” i.e. bond stretching therefore … C m =3R

Molecular Velocity and Energy Distribution Term “average velocity” used to this point … therefore a range of velocity values exists… i.e. VELOCITY DISTRIBUTION Velocities from zero (at collision) to larger values … The Velocity Distribution is described by the Maxwell-Boltzmann distribution function

With n E being the number of molecules per unit volume per unit energy at an energy E! … last term is know as the BOLTZMANN factor Atoms have a range of energies BUT a mean energy of 3/2kT ! And another important GENERAL relationship – the PROBABILITY that a certain molecule in a given system will have an energy E Maxwell-Boltzmann Distribution for Translational Energies (monatomic gas)

Thermally Activated Processes Arrhenius Behavior … where the rate of change is proportional to: The Energy E A is “characteristic” of the particular process What are the consequences of high E A or raising the temperature?

Thermally Activated Processes Fig 1.29

Fig 1.30

Thermally Activated Processes DIFFUSION … ?? E A for P diffusion in Si is 3.69 eV D is the diffusion coefficient … and D O is a constant (10.5 cm 2 /s) Rms distance in t seconds is … WATCH out for the units … Start using eV for energy … And K for Temperature kT at room temp. is eV D(RT)=1.08x cm 2 /s …in 5 minutes … L(RT)=8.04x μm L(200C)=1.74x μm L(800C)= μm L(1100C)=0.134 μm

Thermally Activated Processes DIFFUSION … ?? E A for P diffusion in Si is 3.69 eV D is the diffusion coefficient … and D O is a constant (10.5 cm 2 /s) Rms distance in t seconds is … WATCH out for the units … Start using eV for energy … And K for Temperature kT at room temp. is eV D(RT)=1.08x cm 2 /s …in 5 minutes … L(RT)=8.04x μm L(200C)=1.74x μm L(800C)= μm L(1100C)=0.134 μm

n v = vacancy concentration N = number of atoms per unit volume E v = vacancy formation energy … also a thermally activated process Equilibrium Concentration of Vacancies

Phase and Phase Diagram Phase: a HOMOGENEOUS portion of a chemical system that has same structure, composition and properties everywhere. Phase Diagram: A Temp vs Phase diagram in which various phases of a system are identified by lines and regions. 100% Cu 100% Ni