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

Solid-State Electronics Chap. 1

Instructor: Pei-Wen LiDept. of E. E. NCU

1

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%



2

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　



3

Chap 1. Solid State Electronics: A General Introduction

Introduction Classification of materials Crystalline and impure semiconductors Crystal lattices and periodic structure Reciprocal lattice



4

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.



5

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 High Medium Low

Hardness High Medium Low



6

Classification Schemes of Solids

Geometry (Crystallinity v.s. Imperfection) Purity (Pure v.s. Impure) Electrical Classification (Electrical Conductivity) Mechanical Classification (Binding Force)



7

Geometry

Crystallinity– Single crystalline, polycrystalline, and amorphous



8

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:



9

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.



10

Electrical Conductivity

Material type Resistivity

(-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,



11

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.



12

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.



13

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:1. To provide a wide range of conductivity (III- B or V-P in Si).2. 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.



14

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



15

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.

b̂



16

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

Unit Cell



17

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>



18

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



19

Example Use of Miller Indices

Wafer Specification (Wafer Flats)



20

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.



21

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



22

Basic Cubic Lattice

Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC)



23

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 =

)2)((

atoms 2

11 aa



24

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

=109.4oo

ba

ba

ba

4.109)3

1(cos,

|||cos

)4

1,

4

1,

4

1(),

4

1,

4

1,

4

1(

11

)0,0,0( )4

1,

4

1,

4

1(

)4

1,

4

1,

4

1(



25

Diamond Structure

Or the diamond could be visualized by a bcc with four of the corner atoms missing.



26

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.



27

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.



28

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.

cba ˆ ,ˆ ,ˆCBA ˆ ,ˆ ,ˆ

cba

baC

cba

acB

cba

cbA

ˆxˆˆ

ˆxˆ2ˆ ;

ˆxˆˆ

ˆxˆ2ˆ ;

ˆxˆˆ

ˆxˆ2ˆ



29

Diffraction

Definition of scattering vector



30

Reciprocal Lattice

kIncident x-ray

beam vector,

'k

Outing beam vector

Reciprocal lattice vector G

kkG

'



31

Example

Consider a BCC lattice and its reciprocal lattice (FCC)

Similarly, the reciprocal lattice of an FCC is BCC lattice.

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

Documents

Transcript of Solid-State Electronics Chap. 1 Instructor: Pei-Wen Li Dept. of E. E. NCU 1 Solid-State Electronics ...