Sinai University Faculty of Engineering Science Department of Basic science

1. Sinai University Faculty of Engineering Science Department of Basic science W1

2. Text Book: Principles of Electronic Materials and Devices, 3rd edition, Safa Kasap Lecture name Ch 1-2 Crystal structure W3

3. 1.7 Thermally Activated Process1.7.1 Arrhenius Rate Equation Arrhenius type behavior Rate of change of any physical or chemical process is proportional to exp(EA/kT) EA is a characteristic energy parameter W3

4. Example W3

5. 1.7 Thermally Activated ProcessExample W3

6. Example: Diffusion of an interstitial impurity atom A* PE, EA A B Displacement , X W3

7. 1.7 Thermally Activated Process1.7.1 Arrhenius Rate Equation N Total number of impurities According 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)  = Avexp(EA/kT), rate of jumps=1/t EA = UA*UA = 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. W3

8. 1.7.2 Atomic diffusion and the diffusion coefficient a is the closest distance between voids X2 = a2cos2q1+ a2cos2q2+ …..+Na2cos2qN X2 = ½ a2N L2=X2+Y2 =a2N An impurity atom has four site choices for diffusion to a neighboring interstitial interstitial vacancy. After N jumps, the impurity atom would have been displaced from the original position at O. W3

9. Mean Square Displacement • = Av exp(EA/kT)= frequency=1/t • t=N L2 = a2t = 2Dt L = “distance” diffused after time t, a = closest void to void separation (jump distance),= frequency of jumps, t = time, D = diffusion coefficient Diffusion coefficient is thermally activated D = diffusion coefficient, DO = constant, EA = activation energy, k = Boltzmann constant, T = temperature Example 1.12 W3

10. 1.8 Crystal Structures Cubic FeS2, iron sulfide, or pyrite, crystals. The crystals look brass-like yellow (“fool’s gold”). |SOURCE: Photo by SOK Galena is lead sulfide, PbS, and has a cubic crystal structure |SOURCE: Photo by SOK A crystalline solid is a solid in which atoms bond with each other in a rectangular form to form a periodic collection of atoms It has a long range order Predicts the atomicarrangement any where in the crystal. W3

11. CRYSTALS Nearly all metals, many ceramics and semiconductors, various polymers are crystalline solids (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. W3

12. Lattice parameters, a,b,c, a,b,g W3

13. The seven crystal systems (unit cell geometries) and fourteen Bravais lattices. W3

14. FCC Volume of atoms in a cubic unit cell= 74%. This is the maximum packing possible with identical sphere (a) The crystal structureof copper is face centered cubic (FCC). The atoms are positioned at 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. W3

15. BCC Volume of atoms in a cubic unit cell= 68%. • 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 BCC unit cell with closely packed hard spheres representing the Fe atoms. • A reduced-sphere unit cell. W3

16. 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

17. 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

18. 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

19. 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. Packing of coins on a table top to build a two dimensional crystal W3

20. Example 1.13 The FCC unit cell. The atomic radius is R and the lattice parameter is a W3

21. When anion and cation has the same size, CsCl structure A possible reduced sphere unit cell for the CsCl crystal. An alternative unit cell may have Cs+ and Cl- interchanged. Examples: CsCl, CsBr, CsI, TlCl, TlBr, TlI. Assignment: Why it is not BCC? W3

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23. 1.9 Crystalline defects and their significance 1.9.1 Point defects: Vacancies and Impurities Generation of a vacancy by the diffusion of atom to the surface and the subsequent diffusion of the vacancy into the bulk. W3

24. 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 W3

25. Point defects in the crystal structure. The regions around the point defect become distorted; the lattice becomes strained. W3

26. Assignment Solve problems 1.19- 1.21- 1.23- 1.30 W3