Sinai University Faculty of Engineering Science Department of Basic science

04/21/23 1W1

Text Book: Principles of Electronic Materials

and Devices, 3rd edition, Safa Kasap

Lecture nameCh 1-2 Crystal structure

04/21/23 W3 2

04/21/23 3

Arrhenius type behavior

Rate of change of any physical or chemical process is

proportional to

exp(EA/kT)

EA is a characteristic energy parameter

1.7 Thermally Activated Process1.7.1 Arrhenius Rate Equation

W3

Example

04/21/23 4W3

1.7 Thermally Activated ProcessExample

04/21/23 5W3

Example: Diffusion of an interstitial impurity atom

04/21/23 6

BA

A*

PE

, E

A

Displacement , X

W3

1.7 Thermally Activated Process1.7.1 Arrhenius Rate Equation

= frequency of jumps, A = a dimensionless constant that has only a weak temperature dependence, vo = vibrational

frequency, EA = activation energy, k = Boltzmann constant, T = temperature, UA* = potential energy at the activated state A*,

UA = potential energy at state A.

= Av exp(EA/kT), rate of jumps=1/t

EA = UA* UA

04/21/23 7

N Total number of impuritiesAccording to Boltzmann distribution: nEdE will have KE in the range E to E+dE

The probability that an impurity atom has an energy E greater than EA Probability ( E>EA)= Number of imprities with E > EA/ N

=∫nEdE/N= A exp(-EA/kT)

W3

Fig 1.30

An impurity atom has four site choices for diffusion to a neighboring interstitial interstitial vacancy. After N jumps, the impurity atom would have been displacedfrom the original position at O.

1.7.2 Atomic diffusion and the diffusion coefficient

a is the closest distance between voids

X2 = a2cos21+ a2cos22+ …..+Na2cos2N

X2 = ½ a2NL2=X2+Y2

=a2N

W3

Mean Square Displacement

L = “distance” diffused after time t, a = closest void to void separation (jump distance), = frequency of jumps, t = time, D

= diffusion coefficient

L2 = a2t = 2Dt

Diffusion coefficient is thermally activated

kT

EDaD A

o exp221

D = diffusion coefficient, DO = constant, EA = activation energy, k = Boltzmann constant, T = temperature

04/21/23 9

= Av exp(EA/kT)= frequency=1/t

t=N

Example 1.12W3

1.8 Crystal Structures

Galena is lead sulfide, PbS, and has a cubic crystal structure

|SOURCE: Photo by SOK

Cubic FeS2, iron sulfide, or pyrite, crystals. The crystals look brass-like yellow (“fool’s gold”).

|SOURCE: Photo by SOK

04/21/23 10

A crystalline solid is a solid in which atoms bond with each other in a rectangular form to form a periodic collection of atomsIt has a long range order Predicts the atomic arrangement any where in the crystal.W3

Fig 1.71

(a) A simple square lattice. The unit cell is a square with a side a.(b) Basis has two atoms.(c) Crystal = Lattice + Basis. The unit cell is a simple square with two atoms.(d) Placement of basis atoms in the crystal unit cell.

CRYSTALSNearly all metals, many ceramics and semiconductors, various polymers are crystalline solids

W3

Fig 1.31

Lattice parameters, a,b,c, a,b,g

W3

Fig 1.72

The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.

W3

Fig 1.31

(a) The crystal structure of copper is face centered cubic (FCC). The atoms are positionedat well defined sites arranged periodically and there is a long range order in the crystal.(b) An FCC unit cell with closed packed spheres. (c) Reduced sphere representation of the unit cell. Examples: Ag, Al, Au, Ca, Cu, γ-Fe (>912 ˚C), Ni, Pd, Pt, Rh.

FCC

W3

Volume of atoms in a cubic unit cell= 74%. This is the maximum packing possible with identical sphere

Fig 1.32

Body centered cubic crystal (BCC) crystal structure.Example: Alkali metals (Li, Na, K, Rb), Cr, Mo, W, Mn, α-Fe (< 912 ˚C), β-Ti (> 882 ˚C)(a) A BCC unit cell with closely packed hard spheres representing the Fe atoms.(b) A reduced-sphere unit cell.

BCC

W3

Volume of atoms in a cubic unit cell= 68%.

Fig 1.33

The Hexagonal Close Packed (HCP) Crystal Structure. (a) The Hexagonal Close Packed (HCP) Structure. A collection of many Zn atoms. Color difference distinguishes layers (stacks).(b) The stacking sequence of closely packed layers is ABAB (c) A unit cell with reduced spheres (d) The smallest unit cell with reduced spheres.

W3

Fig 1.34

The diamond unit cell is cubic. The cell has eight atoms. Grey Sn (α-Sn) and the Elemental semiconductors Ge and Si have this crystal structure.

W3

Fig 1.35

The Zinc blende (ZnS) cubic crystal structure. Many important compound crystal Structures have the zinc blende structure. Examples: AlAs, GaAs, Gap, GaSb, InAs, InP,InSb, ZnS, ZnTe.

W3

Fig 1.36

Packing of coins on a table top to build a two dimensional crystal

W3

The importance of the size effect

A possible reduced sphere unit cell for the NaCl (rock salt) crystal. An alternative Unit cell may have Na+ and Cl- interchanged. Examples: AgCl, CaO, CsF, LiF, LiCl, NaF, NaCl, KF, KCl, MgO.

Fig 1.39

The FCC unit cell. The atomic radius is R and the lattice parameter is a

W3

Example 1.13

Fig 1.38

A possible reduced sphere unit cell for the CsCl crystal. An alternative unit cell may haveCs+ and Cl- interchanged. Examples: CsCl, CsBr, CsI, TlCl, TlBr, TlI.

W3

When anion and cation has the same size, CsCl structure

Assignment:Why it is not BCC?

04/21/23 22W3

Fig 1.44

Generation of a vacancy by the diffusion of atom to the surface and the subsequent diffusionof the vacancy into the bulk.

1.9 Crystalline defects and their significance1.9.1 Point defects: Vacancies and Impurities

W3

Equilibrium Concentration of Vacancies

nv = vacancy concentration

N = number of atoms per unit volume

Ev = vacancy formation energy

k = Boltzmann constant

T = temperature (K)

Examples 1.15 and 1.16

nv N exp Ev

kT

04/21/23 24W3

Fig 1.45

Point defects in the crystal structure. The regions around the point defect become distorted; the lattice becomes strained.

W3

Assignment

Solve problems

1.19- 1.21- 1.23- 1.30

Fig 1.31

W3