EEE-3515 Electrical Properties of Materials Dr. (Ph.D) Mohammad Aminul Islam International Islamic University Chittagong Department of Electrical and Electronic Engineering

Book Reference 1. Solid state Electronic Device - Ben G. Stretman & Sanjay Kumar Banerjee 2. Principles of Electronic Materials and Devices - S.O. Kasap

CH# 1 Crystal Properties  Semiconductor & Semiconductor Materials  Crystal  Types of Crystals  Lattice & Basis  Bravias Lattice and  Miller Indices

CH# 1, Lecture 1 OUTLINE  Introduction to the Semiconductor How do atoms ARRANGE themselves to form solids? Types of solids  Crystalline Materials o Single crystal o Polycrystalline  Amorphous Unit cells Crystal structures o Face-centered cubic o Body-centered cubic o Hexagonal close-packed Close packed crystal structures Density

Why Study Solid State Physics?

Periodic table: where the semiconductor Materials are? IIIIIIVVVI B Boron C Carbon N Nitrogen O Oxygen Al Aluminum Si Silicon P Phosphorus S Sulfur Zn Zinc Ga Galium Ge Germanium As Arsenic Se Selenium Cd Cadmium In Indium Sn Tin Sb Antimony Te Tellurium

Semiconductor Materials o Element : Si, Ge o IV compounds : SiC, SiGe o III-V compounds: AIP, AlAs, AlSb, GaN,GaP, GaAs, GaSb, InP, InAs, InSb o II-VI: SnS, ZnSe, ZnTe, CdS, CdSe, CdTe o LED(GaN, GaP, GaAs), Three-elements(GaAsP, InGaAsP), Fluorescent(II-VI, ZnS), Light detector(InSb, CdSe), PbTe, HgCdTe, Si, Ge) IIIIIIVVVI B Boron C Carbon N Nitrogen O Oxygen Al Aluminum Si Silicon P Phosphorus S Sulfur Zn Zinc Ga Galium Ge Germanium As Arsenic Se Selenium Cd Cadmium In Indium Sn Tin Sb Antimony Te Tellurium

In Semiconductor production, doping is the process of intentionally introducing impurities into an extremely pure (also referred to as intrinsic) semiconductor in order to change its electrical properties. The number of dopant atoms needed to create a difference in the ability of a semiconductor to conduct is very small. Where a comparatively small number of dopant atoms are added (of the order of 1 every 100,000,000 atoms) then the doping is said to be low, or light. Where many more are added (of the order of 1 in 10,000) then the doping is referred to as heavy, or high. This is often shown as n+ for n-type dopant or p+ for p-type doping.

9 Types of Solids (a) Crystalline material: periodic array (i) Single crystal: periodic array over the entire extent of the material (ii) Polycrystalline material: many small crystals or grains (b) Amorphous: lacks a systematic atomic arrangement CrystallineAmorphous SiO 2

10 Crystal Structure Consider atoms as hard spheres with a radius. Shortest distance between two atoms is a diameter. Crystal described by a lattice of points at center of atoms

11 Unit Cell The unit cell is building block for crystal. Repetition of unit cell generates entire crystal. Ex: 2D honeycomb represented by translation of unit cell Ex: 3D crystalline structure

Another Definition of Unit cell A small cell in the crystal structure that carries the prope rties of the crystal. The repetition of the unit cell in 3-di mensions generated the whole crystal structure. In the cubic crystal system three types of arrangements are found: –Simple cubic –Body-centered cubic –Face-centered cubic

13 Metallic Crystal Structures  Metals usually polycrystalline amorphous metal possible by rapid cooling  Bonding in metals non-directional  large number of nearest neighbors and dense atomic packing  Atom (hard sphere) radius, R: defined by ion core radius: ~ nm  Most common unit cells Faced-centered cubic (FCC) Body-centered cubic (BCC) Hexagonal close-packed (HCP).

Cubic Lattice The simple cubic (a), the body-centered cubic (b) and the face centered cubic (c) lattice. Since all unit vectors identifying the traditional unit cell have the same size, the crystal structure is completely defined by a single number. This number is the lattice constant, a.

Coordination # = 6 (# nearest neighbors) SIMPLE CUBIC a R=1/2*a a a

SIMPLE CUBIC

17 Face-Centered Cubic (FCC) Crystal Structure (I)  Atoms located at corners and on centers of faces  Cu, Al, Ag, Au have this crystal structure Two representations of the FCC unit cell

18  Hard spheres touch along diagonal  the cube edge length, a= 2R  2  The coordination number, CN = number of closest neighbors = number of touching atoms, CN = 12  Number of atoms per unit cell, n = 4. FCC unit cell: 6 face atoms shared by two cells: 6 x 1/2 = 3 8 corner atoms shared by eight cells: 8 x 1/8 = 1  Atomic packing factor, APF = fraction of volume occupied by hard spheres = (Sum of atomic volumes)/(Volume of cell) = 0.74 (maximum possible) Face-Centered Cubic Crystal Structure (II) R a

ATOMIC PACKING FACTOR Fill a box with hard spheres –Packing factor = total volume of spheres in box / volume of box –Question: what is the maximum packing fa ctor you can expect? In crystalline materials: –Atomic packing factor = total volume of ato ms in unit cell / volume of unit cell –(as unit cell repeats in space)

5 APF for a simple cubic structure = 0.52 Adapted from Fig. 3.19, Callister 6e. ATOMIC PACKING FACTOR

21  = mass/volume = (atoms in the unit cell, n ) x (mass of an atom, M) / (the volume of the cell, V c ) Density Computations Atoms in the unit cell, n = 4 (FCC) Mass of an atom, M = A/N A A = Atomic weight (amu or g/mol) Avogadro number N A =  atoms/mol The volume of the cell, V c = a 3 (FCC) a = 2R  2 (FCC) R = atomic radius

22  Hard spheres touch along cube diagonal  cube edge length, a= 4R/  3  The coordination number, CN = 8  Number of atoms per unit cell, n = 2 Center atom not shared: 1 x 1 = 1 8 corner atoms shared by eight cells: 8 x 1/8 = 1  Atomic packing factor, APF = 0.68  Corner and center atoms are equivalent Body-Centered Cubic Crystal Structure (II) a

23 Hexagonal Close-Packed Crystal Structure (I)  Six atoms form regular hexagon surrounding one atom in center  Another plane is situated halfway up unit cell (c-axis) with 3 additional atoms situated at interstices of hexagonal (close-packed) planes  Cd, Mg, Zn, Ti have this crystal structure

24  Unit cell has two lattice parameters a and c. Ideal ratio c/a =  The coordination number, CN = 12 (same as in FCC)  Number of atoms per unit cell, n = 6. 3 mid-plane atoms not shared: 3 x 1 = 3 12 hexagonal corner atoms shared by 6 cells: 12 x 1/6 = 2 2 top/bottom plane center atoms shared by 2 cells: 2 x 1/2 = 1  Atomic packing factor, APF = 0.74 (same as in FCC) Hexagonal Close-Packed Crystal Structure (II) a c

25 Density of a crystalline material,  = density of the unit cell = (atoms in the unit cell, n )  (mass of an atom, M) / (the volume of the cell, V c ) Density Computations Summarized Atoms in unit cell, n = 2 (BCC); 4 (FCC); 6 (HCP) Mass of atom, M = Atomic weight, A, in amu (or g/mol). Translate mass from amu to grams divide atomic weight in amu by Avogadro number N A =  atoms/mol Volume of the cell, V c = a 3 (FCC and BCC) a = 2R  2 (FCC); a = 4R/  3 (BCC) where R is the atomic radius Atomic weight and atomic radius of elements are in the table in textbook front cover.

26  Corner and face atoms in unit cell are equivalent  FCC has APF of 0.74 Maximum packing  FCC is close-packed structure  FCC can be represented by a stack of close-packed planes (planes with highest density of atoms) Face-Centered Cubic Crystal Structure (III)

27  FCC and HCP: APF =0.74 (maximum possible value)  FCC and HCP may be generated by the stacking of close-packed planes  Difference is in the stacking sequence Close-packed Structures (FCC and HCP) HCP: ABABAB... FCC: ABCABCABC…

28 HCP: Stacking Sequence ABABAB... Third plane placed directly above first plane of atoms

29 FCC: Stacking Sequence ABCABCABC... Third plane placed above “holes” of first plane not covered by second plane

30 Some materials can exist in more than one crystal structure, Called polymorphism. If material is an elemental solid: called allotropy. Ex: of allotropy is carbon: can exist as diamond, graphite, amorphous carbon. Polymorphism and Allotropy Pure, solid carbon occurs in three crystalline forms – diamond, graphite; and large, hollow fullerenes. Two kinds of fullerenes are shown here: buckminsterfullerene (buckyball) and carbon nanotube.

31 Single Crystals and Polycrystalline Materials Single crystal: periodic array over entire material Polycrystalline material: many small crystals (grains) with varying orientations. Atomic mismatch where grains meet (grain boundaries) Grain Boundary

32 Polycrystalline Materials Atomistic model of a nanocrystalline solid

33 Polycrystalline Materials Simulation of annealing of a polycrystalline grain structure

34 Anisotropy Different directions in a crystal have different packing. For instance: atoms along the edge of FCC unit cell are more separated than along the face diagonal. Causes anisotropy in crystal properties Deformation depends on direction of applied stress If grain orientations are random  bulk properties are isotropic Some polycrystalline materials have grains with preferred orientations (texture): material exhibits anisotropic properties

35 Non-Crystalline (Amorphous) Solids Amorphous solids: no long-range order Nearly random orientations of atoms (Random orientation of nano-crystals can be amorphous or polycrystalline) Schematic Diagram of Amorphous SiO 2

36 Summary  Allotropy  Amorphous  Anisotropy  Atomic packing factor (APF)  Body-centered cubic (BCC)  Coordination number  Crystal structure  Crystalline  Face-centered cubic (FCC)  Grain  Grain boundary Make sure you understand language and concepts:  Hexagonal close-packed (HCP)  Isotropic  Lattice parameter  Non-crystalline  Polycrystalline  Polymorphism  Single crystal  Unit cell