ECE230A_Crystal_structure-230A

ECE230A_Crystal_structure-230A - Solid Solid State...

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Solid State Electronics ECE230A Lecture Notes Professor Yu-Hwa Lo 1

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ontents Contents Crystal Structure of Solids Quantum Theory and Energy Band Equilibrium Carrier Statistics Carrier Transport Generation and Recombination Excess Carriers in Semiconductors PN Junction 2
Section 1. rystal Structure of Solids Crystal Structure of Solids 3

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Crystal Structure Crystal structure is a unique arrangement of atoms in a crystal. It is composed of a unit cell which is a set of toms arranged in a particular way and atoms arranged in a particular way, and periodically repeated in three dimensions on ttice a lattice . A crystal’s structure and symmetry play important role in determining the cleavage, pg g, electronic band structure, and optical properties of the crystal. 4
Unit Cell Concept A unit cell is a small portion of any given crystal that can be used to reproduce the crystal. For each crystal structure, there is a conventional unit cell which is the smallest unit that has the full symmetry of the crystal. Conventional unit cell is not the smallest possible. primitive unit cell is the smallest possible unit cell one can construct such that when tiled, it completely fills space; but it does not display all e symmetries inherent in the crystal 5 the symmetries inherent in the crystal.

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Unit Cell Concept The unit cell and the lattice it characterizes can be described in terms of basis vectors . rh a k b =+ v v v In 2-D, we have: h a k b l c + + v v vv 3 we have: In 3-D, we have: 6
Bravais Lattices Bravais lattices describe the geometric arrangement of the lattice points , and thereby the translational symmetry of the crystal . In 3-D, there are 14 unique Bravais lattices hich are distinct from one another in the which are distinct from one another in the translational symmetry they contain. 7

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Bravais Lattices Here are the 14 unique Bravais lattices. Simple cubic Body-centered cubic Face-centered cubic 8
Bravais Lattices Triclinic Simple monoclinic Base-centered monoclinic imple orthorhombic Base-centered Body-centered 9 Simple orthorhombic orthorhombic y orthorhombic

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Bravais Lattices Trigonal Hexagonal Face-centered orthorhombic imple tetragonal ody entered tetragonal 10 Simple tetragonal Body-centered tetragonal
Crystal Systems All real crystals fall into one of seven groupings . ystem ymmetry System Symmetry Triclinic None onoclinic ne 2 ld rotation axis Monoclinic One 2-fold rotation axis Orthorhombic Three mutually perpendicular 2-fold rotation axes Tetragonal One 4-fold rotation axis or a 4-fold rotation- inversion axis Cubic Four 3-fold rotation axes (cube diagonals) (g ) Hexagonal One 6-fold rotation axis Trigonal (Rhombohedral) One 3-fold rotation axis 11 g( )

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Semiconductor Lattices In Si and Ge , the lattice structure is described by two interpenetrating FCC lattices as diamond lattice unit cell .
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