Sinai University Faculty of Engineering Science Department of Basic science 6/11/20151W1

Text Book: Principles of Electronic Materials and Devices, 3 rd edition, Safa Kasap Lecture name Ch 1-2 Crystal structure 6/11/2015W32

6/11/20153 Arrhenius type behavior Rate of change of any physical or chemical process is proportional to exp(  E A /kT) E A is a characteristic energy parameter 1.7 Thermally Activated Process Arrhenius Rate Equation W3

Example 6/11/20154W3

1.7 Thermally Activated Process Example 6/11/20155W3

Example: Diffusion of an interstitial impurity atom 6/11/20156 BA A*A* PE, E A Displacement, X W3

1.7 Thermally Activated Process Arrhenius Rate Equation = frequency of jumps, A = a dimensionless constant that has only a weak temperature dependence, v o = vibrational frequency, E A = activation energy, k = Boltzmann constant, T = temperature, U A* = potential energy at the activated state A*, U A = potential energy at state A. = Av  exp(  E A /kT), rate of jumps=1/t E A = U A*  U A 6/11/20157 N Total number of impurities According to Boltzmann distribution: n E dE will have KE in the range E to E+dE The probability that an impurity atom has an energy E greater than E A Probability ( E>E A )= Number of imprities with E > E A / N = ∫n E dE/N= A exp(-E A /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 displaced from the original position at O Atomic diffusion and the diffusion coefficient a is the closest distance between voids X 2 = a 2 cos 2  1 + a 2 cos 2  2 + …..+Na 2 cos 2  N X 2 = ½ a 2 N L 2 =X 2 +Y 2 =a 2 N 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 L 2 = a 2 t = 2Dt Diffusion coefficient is thermally activated D = diffusion coefficient, D O = constant, E A = activation energy, k = Boltzmann constant, T = temperature 6/11/20159 = Av  exp(  E A /kT)= frequency=1/t t=N Example 1.12 W3

1.8 Crystal Structures Galena is lead sulfide, PbS, and has a cubic crystal structure |SOURCE: Photo by SOK Cubic FeS 2, iron sulfide, or pyrite, crystals. The crystals look brass-like yellow (“fool’s gold”). |SOURCE: Photo by SOK 6/11/ 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 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. CRYSTALS Nearly all metals, many ceramics and semiconductors, various polymers are crystalline solids W3

Fig 1.31 Lattice parameters, a,b,c,   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 positionedstructure 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. 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 ( 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 have Cs + 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?

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Fig 1.44 Generation of a vacancy by the diffusion of atom to the surface and the subsequent diffusion of the vacancy into the bulk. 1.9 Crystalline defects and their significance Point defects: Vacancies and Impurities W3

Equilibrium Concentration of Vacancies n v = vacancy concentration N = number of atoms per unit volume E v = vacancy formation energy k = Boltzmann constant T = temperature (K) Examples 1.15 and /11/201524W3

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 Fig 1.31 W3