sinai university faculty of engineering science department of basic science
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Sinai University Faculty of Engineering Science Department of Basic science. Text Book: Principles of Electronic Materials and Devices, 3 rd edition, Safa Kasap Lecture name. Ch 1-2 Crystal structure. 1.7 Thermally Activated Process 1.7.1 Arrhenius Rate Equation. Arrhenius type behavior - PowerPoint PPT PresentationTRANSCRIPT
Sinai University Faculty of Engineering Science Department of Basic science
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Text Book: Principles of Electronic Materials
and Devices, 3rd edition, Safa Kasap
Lecture nameCh 1-2 Crystal structure
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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
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Example
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1.7 Thermally Activated ProcessExample
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Example: Diffusion of an interstitial impurity atom
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BA
A*
PE
, E
A
Displacement , X
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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
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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)
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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
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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
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= 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
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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
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Fig 1.31
Lattice parameters, a,b,c, a,b,g
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Fig 1.72
The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.
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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
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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
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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.
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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.
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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.
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Fig 1.36
Packing of coins on a table top to build a two dimensional crystal
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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
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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.
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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 diffusionof the vacancy into the bulk.
1.9 Crystalline defects and their significance1.9.1 Point defects: Vacancies and Impurities
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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
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Fig 1.45
Point defects in the crystal structure. The regions around the point defect become distorted; the lattice becomes strained.
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Assignment
Solve problems
1.19- 1.21- 1.23- 1.30
Fig 1.31
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