Solid State Device Fundamentals

Transcription

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

2 Interatomic bonding Bonding Forces and Energies Equilibrium atomic spacing Minimization of bonding energy Types of Bonding Ionic Covalent Secondary Metallic 2

3 Bonding forces Interatomic Forces attractive forces, F a (x) repulsive forces, F r (x) When the atoms reach a critical distance (x 0 ), the attractive and repulsive forces cancel each other and the atoms are at their equilibrium distance. 3

4 Bonding energy Sometimes it is easier to deal with potential energies (E) rather than forces. The relation of Energy to Force is as follows: E r F dr EA ER Equilibrium is reached by minimizing potential energy E. 4

5 Ionic bonding Most common bonding in metal-nonmetal compounds. Atoms give up/receive electrons from other atoms in the compound to form stable electron configurations Because of net electrical charge in each ion, they attract each other and bond via coulombic forces. 5

6 Ionic bonding forces Attractive and repulsive energies are functions of interatomic distance and may be represented as follows: E E A B A r B n r A and B are constants depending upon the atomic system. The value of n is usually taken as 12. 6

7 Properties of ionic bonding Nondirectional forces: magnitude of bond is equal in all directions around the ion. High bonding energies (~ kj/mol). reflected in high melting temperatures Generally hard and brittle materials. most common bonding for ceramic materials Electrically and thermally insulating materials. 7

8 Covalent bonding Stable configurations are obtained by the sharing of valence electrons by 2 or more atoms. Typical in nonmetallic compounds (CH 4, H 2 0) Number of possible bonds per atom is determined by the number of valence electrons in the following formula: number of bonds = 8 - (valence electrons) Bonds also are angle dependent. 8

9 Properties of covalent bonding Depending upon the atoms involved, covalent bonding can be either very strong, or very weak. This is also reflected in the melting temperature of the covalent bonded substances: - diamond (strong bond) - T m > 3350 C - silicon (strong bond) T m = 1414 C - bismuth (weak bond) -- T m ~ 270 C Covalent bonding is the most common form of bonding in polymers. Ethane Molecule Polyethylene chain 9

10 Solids Three types of solids classified according to atomic arrangement: Crystalline Polycrystalline 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. 10

11 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 2 repeats in each direction (b). Different unit cells of cubic lattice: primitive, body-centered, face-centered. Example of a complex cubic lattice: Silicon crystal lattice. 11

12 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 Silicon crystal has so-called diamond type lattice. Each Si atom has 4 nearest neighbors. Diamond lattice starts with a FCC lattice and then adds four additional INTERNAL atoms at locations r = a/4+b/4+c/4 away from each of the atoms. In other words, diamond lattice is formed by two FCC lattices sifted by the vector r. 12

13 Crystallographic positions in Si crystal What are the positions of the blue atoms in silicon unit cell? Find interatomic distance for Si lattice. Tetrahedron 13

14 Homework 4 Crystallographic positions Identify crystallographic position of all atoms in silicon unit cell. 14

15 Crystallographic directions Crystallographic direction is a direction between any two atoms of crystal lattice [112] Hexagonal lattice Family of directions: e.g. [123], [213], [312], [132], [231], [321] for cubic lattice. In the cubic lattice directions having the same indices regardless of order or sign are equivalent. Dot product of indices of two perpendicular directions is zero. Directions [100] and [010] are perpendicular: [100] [010]=0 15

16 Finding crystallographic direction 16

17 Homework 5 Crystallographic directions in Si crystal Identify crystallographic directions from red atom towards all atoms in silicon unit cell. Are directions of electronic bonds (blue bonds) perpendicular? 17

18 Crystallographic planes Crystallographic planes are denoted by Miller indices /3 1/5 1/ (535) In the cubic system, a plane and a direction with the same indices are orthogonal. E.g. [100] direction is perpendicular to (100) plane. Correspondingly, [123] direction is perpendicular to (123) plane. Indices of crystallographic plane can be found from cross product of indices of any two non-parallel directions in this plane. 18

19 Homework 6 Crystallographic planes in Si crystal Identify crystallographic planes comprising red atom and any two of the blue atoms in silicon unit cell. Find directions perpendicular to these planes. 19

20 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. a There is a tendency: The higher direction indices the lower linear density. LAD [100] = ( )/a = 1/a LAD [110] = ( )/ 2a = 1/ 2a = 0.71/a LAD [111] = ( )/ 3a = 1/ 3a = 0.58/a LAD [111]BCC = ( )/ 3a = 2/ 3a = 1.15/a 20

21 Homework 7 LAD of crystallographic directions in Si crystal Calculate LAD in silicon along [120], [123] and [112] directions. 21

22 Atomic density of crystallographic planes Atomic Density (AD) of crystallographic planes is measured by number of atoms per unit area. Tendency: The higher Miller indices the lower atomic density. 22

23 Homework 8 Atomic density of crystallographic planes in Si crystal Calculate AD in silicon for planes (120), (123) and (112). 23

24 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. 24

25 Homework 9 APF of Si crystal lattice Calculate APF of silicon lattice. 25

26 0D defects (point defects) Defects in crystals 1D defects (linear defects) 3D defects (bulk defects) 2D defects (planar defects) 17