Solid State Device Fundamentals

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1 Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev Tel: Office 4N101b 1

2 Solids Three types of solids, classified according to atomic arrangement Crystalline Polyscrystalline Amorphous Crystal is a periodic atomic structure. This structure can be reproduced by translation of an elementary element which is known as unit cell. The least translation along one axis is known as lattice parameter. 2

3 Crystal lattice There are 7 types of crystal lattices (called Bravais lattices), shown below: The unit cell of a simple cubic lattice (a) along with an image of 4 repeats in each direction (b). Different unit cells of cubic lattice: primitive, body-centered, face-centered. Example of a complex cubic lattice: Si crystal lattice. 3

4 Crystallographic positions Crystallographic position is denoted by three numbers, which are coefficients of the position vector, e.g. ½ ½ ½ for the red atom in the example above. Silicon crystal has so-called diamond type lattice. Each Si atom has 4 nearest neighbors 4

5 Crystallographic positions in Si crystal What are the positions of the blue atoms in silicon unit cell? Tetrahedron 5

6 Crystallographic directions Crystallographic direction is a direction between any two atoms of crystal lattice Cubic lattice [221] Hexagonal lattice 6

7 Crystallographic directions in Si crystal What are the directions from red atom towards blue atoms in silicon unit cell? 7

8 Crystallographic planes Crystallographic planes are denoted by Miller indices /3 1/5 1/ (535) 8

9 Crystallographic planes in Si crystal What are the crystallographic planes comprising red atom and one of the blue atoms in silicon unit cell? 9

10 Linear atomic density of crystallographic directions Linear Atomic Density (LAD) of a crystallographic direction is measured by number of atoms per unit length along this direction. The higher direction indices the lower linear density. a LAD [100] = ( )/a LAD [110] = ( )/ 2a LAD [111] = ( )/ 3a 10

11 LAD of crystallographic directions in Si crystal Calculate LAD in silicon along [100], [110] and [111] directions. 11

12 Atomic density of crystallographic planes Atomic Density (AD) of crystallographic planes is measured by number of atoms per unit area. The higher Miller indices the lower atomic density. 12

13 AD of crystallographic planes in Si crystal Calculate AD in silicon for planes (100), (110) and (111) directions. 13

14 APF Atomic Packing Factor APF is a proportion of space that would be filled by spheres that are centered on the vertices of the crystal structure and are as large as possible without overlapping. 14

15 APF of Si crystal lattice Show that APF of silicon is 15

16 0D defects (point defects) Defects in crystals 1D defects (linear defects) 3D defects (bulk defects) 2D defects (planar defects) 29

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