Solid-State Electronics Textbook: “Semiconductor Physics and Devices” By Donald A. Neamen, 1997 Reference: “Advanced Semiconductor Fundamentals” By Robert F. Pierret 1987 “Fundamentals of Solid-State Electronics” By C.-T. Sah, World Scientific, 1994 Homework: 0% Midterm Exam: 60% Final Exam: 40% Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Contents Chap. 1 Solid State Electronics: A General Introduction Chap. 2 Introduction to Quantum Mechanics Chap. 3 Quantum Theory of Solids Chap. 4 Semiconductor at Equilibrium Chap. 5 Carrier Motions: Chap. 6 Nonequilibrium Excess Carriers in Semiconductors Chap. 7 Junction Diodes　 Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Chap 1. Solid State Electronics: A General Introduction Classification of materials Crystalline and impure semiconductors Crystal lattices and periodic structure Reciprocal lattice Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Introduction Solid-state electronic materials: Conductors, semiconductors, and insulators, A solid contains electrons, ions, and atoms, ~1023/cm3.  too closely packed to be described by classical Newtonian mechanics. Extensions of Newtonian mechanics: Quantum mechanics to deal with the uncertainties from small distances; Statistical mechanics to deal with the large number of particles. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Classifications of Materials According to their viscosity, materials are classified into solids, liquid, and gas phases. Low diffusivity, High density, and High mechanical strength means that small channel openings and high interparticle force in solids. Solid Liquid Gas Diffusivity Low Medium High Atomic density Hardness Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Classification Schemes of Solids Geometry (Crystallinity v.s. Imperfection) Purity (Pure v.s. Impure) Electrical Classification (Electrical Conductivity) Mechanical Classification (Binding Force) Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Geometry Crystallinity Single crystalline, polycrystalline, and amorphous Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Geometry Imperfection A solid is imperfect when it is not crystalline (e.g., impure) or its atom are displaced from the positions on a periodic array of points (e.g., physical defect). Defect: (Vacancy or Interstitial) Impurity: Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Purity Pure v.s. Impure Impurity: chemical impurities:a solid contains a variety of randomly located foreign atoms, e.g., P in n-Si. an array of periodically located foreign atoms is known as an impure crystal with a superlattice, e.g., GaAs Distinction between chemical impurities and physical defects. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Electrical Conductivity Material type Resistivity (W-cm) Conduction Electron density (cm-3) Examples Superconductor 0 (low T) 0 (high T) 1023 Sn, Pb Oxides Good Conductor 10-6 – 10-5 1022 – 1023 metals: K, Na, Cu, Au Conductor 10-5 – 10-2 1017 – 1022 semi-metal: As, B, Graphite Semiconductor 10-2 – 10-9 106 – 1017 Ge, Si, GaAs, InP Semi-insulator 1010 – 1014 101 – 105 Amorphous Si Insulator 1014 – 1022 1 – 10 SiO2, Si3N4, Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Mechanical Classification Based on the atomic forces (binding force) that bind the atom together, the crystals could be divided into: Crystal of Inert Gases (Low-T solid): Van der Wall Force: dipole-dipole interaction Ionic Crystals (8 ~ 10 eV bond energy): Electrostatic force: Coulomb force, NaCl, etc. Metal Crystals Delocalized electrons of high concentration, (1 e/atom) Hydrogen-bonded Crystals ( 0.1 eV bond energy) H2O, Protein molecules, DNA, etc. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Binding Force Bond energy is a useful parameter to provide a qualitative gauge on whether The binding force of the atom is strong or weak; The bond is easy or hard to be broken by energetic electrons, holes, ions, and ionizing radiation such as high-energy photons and x-ray. In semiconductors, bonds are covalent or slightly ionic bonds. Each bond contains two electrons—electron-pair bond.A bond is broken when one of its electron is removed by impact collision (energetic particles) or x-ray radiation, —dangling bond. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Semiconductors for Electronic Device Application For electronic application, semiconductors must be crystalline and must contain a well-controlled concentration of specific impurities. Crystalline semiconductors are needed so the defect density is low. Since defects are electron and hole traps where e--h+ can recombine and disappear, short lifetime. The role of impurities in semiconductors: To provide a wide range of conductivity (III- B or V-P in Si). To provide two types of charge carriers (electrons and holes) to carry the electrical current , or to provide two conductivity types, n-type (by electrons) and p-type (by holes) Group III and V impurities in Si are dopant impurities to provide conductive electrons and holes. However, group I, II, and VI atoms in Si are known as recombination impurities (lifetime killers)when their concentration is low. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Crystal Lattices A crystal is a material whose atoms are situated periodically on interpenetrating arrays of points known as crystal lattice or lattice points. The following terms are useful to describe the geometry of the periodicity of crystal atoms: Unit cell; Primitive Unit Cell Basis vectors a, b, c ; Primitive Basic vectors Translation vector of the lattice; Rn = n1a +n2b +n3c Miller Indices Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Basis Vectors The simplest means of representing an atomic array is by translation. Each lattice point can be translated by basis vectors, â, , ĉ. Translation vectors: can be mathematically represented by the basis vectors. Rn = n1 â + n2 + n3 ĉ, where n1, n2, and n3 are integers. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Unit Cell Unit cell: is a small volume of the crystal that can be used to represent the entire crystal. (not unique) Primitive unit cell: the smallest unit cell that can be repeated to form the lattice. (not unique) Example: FCC lattice Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Miller Indices To denote the crystal directions and planes for the 3-d crystals. Plane (h k l) Equivalent planes {h k l} Direction [h k l] Equivalent directions <h k l> Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Miller Indices To describe the plane by Miller Indices Find the intercepts of the plane with x, y, and z axes. Take the reciprocals of the intercepts Multiply the lowest common denominator = Mliller indices Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Example Use of Miller Indices Wafer Specification (Wafer Flats) Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

3-D Crystal Structures In 3-d solids, there are 7 crystal systems (1) triclinic, (2) monoclinic, (3) orthorhombic, (4) hexagonal, (5) rhombohedral, (6) tetragonal, and (7) cubic systems. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

3-D Crystal Structures In 3-d solids, there 14 Bravais or space lattices. N-fold symmetry: With 2/n rotation, the crystal looks the same! 6-fold symmetry Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Basic Cubic Lattice Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC) Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Surface Density Consider a BCC structure and the (110) plane, the surface density is found by dividing the number of lattice atoms by the surface area; Surface density = Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Diamond Structure (Cubic System) Most semiconductors are not in the 7 crystal systems mentioned above. Elemental Semiconductos: (C, Si, Ge, Sn) The space lattice of diamond is fcc. It is composed of two fcc lattices displaced from each other by ¼ of a body diagonal, (¼, ¼, ¼ )a lattice constant a =109.4o Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Diamond Structure Or the diamond could be visualized by a bcc with four of the corner atoms missing. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Zinc Blende Structure (Cubic system) Compound Semiconductors: (SiC, SiGe, GaAs, GaP, InP, InAs, InSb, etc) Has the same geometry as the diamond structure except that zinc blende crystals are binary or contains two different kinds of host atoms. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Wurzite Structure (Hexagonal system) Compound Semiconductors (ZnO, GaN, ALN, ZnS, ZnTe) The adjacent tetrahedrons in zinc blende structure are rotated 60o to give the wurzite structure. The distortion changes the symmetry: cubic hexagonal Distortion also increase the energy gap, which offers the potential for optical device applications. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Reciprocal Lattice Every crystal structure has two lattices associated with it, the crystal lattice (real space) and the reciprocal lattice (momentum space). The relationship between the crystal lattice vector ( ) and reciprocal lattice vector ( ) is The crystal lattice vectors have the dimensions of [length] and the vectors in the reciprocal lattice have the dimensions of [1/length], which means in the momentum space. (k = 2/) A diffraction pattern of a crystal is a map of the reciprocal lattice of the crystal. A microscope image, if it could be resolved on a fine enough scale, is a map of the crystal structure in real space. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Diffraction Definition of scattering vector Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Reciprocal Lattice Outing beam vector Reciprocal lattice vector Incident x-ray beam vector, Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1

Example Consider a BCC lattice and its reciprocal lattice (FCC) Similarly, the reciprocal lattice of an FCC is BCC lattice. Instructor: Pei-Wen Li Dept. of E. E. NCU Solid-State Electronics Chap. 1