ECE 209 Notes

Table of Contents

  1. Materials Structure
  2. Atomic Structure
  3. Band Structure
  4. Metals
  5. Optics
  6. Dielectrics
  7. Thermal Properties
  8. Magnetic Properties

Materials Structures

Crystalline, polycrystalline, and amorphous




Crystals in microelectronics

Silicon structure; covalent bonding

Unit cell

Bragg’s Law

- crystal characteristics (and x-ray diffraction) depend on the direction you are looking

Miller indices

Miller Indices for Planes

Miller Indices for Directions

Family of Planes and Directions

Transmission Electron Microscopy

Scanning Tunneling Microscopy

Silicon bulk crystal growth

Epitaxial growth

Molecular beam epitaxy

Epitaxy principles

Modifying Crystals

Ion implantation

Etching and micromachining

Atomic Structure

Nature of light

Experimental Evidence of Light as EM Wave

Photo-emission (photoelectric effect)


Wave-Particle Duality

De Broglie relationship

Electron Diffraction Experiment

Wavefunction, wave vector, and Schrödinger equation

Wave Vector and Potential Energy

Schrodinger’s Equation

“Electron in a box” problem

Electron in a 1D Potential Well

- inside the box, potential energy is zero
- outside, is infinitely large
- we need to find the wave equation

$$ \frac{d^2 \Psi}{dx^2} + \frac{8\pi^2 m}{h^2}(E - V)\Psi = 0 $$

Electron Energy in Potential Well

$$ E = \frac{h^2 n^2}{8mL^2} $$
- energies E(n) are the eigenenergies of the electron
- energy is quantized
- n is the quantum number
- min energy is at n=1, this is the ground state
- energy of electron wave can only have discrete values
- energy of electron particle can take any value

Uncertainty Principle


Hydrogen atom

Atomic Spectra

Quantum Numbers

Principal Quantum Number, n

Orbital Angular Quantum Number, l

Magnetic Quantum Number, m l

Electron Spin Quantum Number, m s

The Full Sert of Quantum Numbers and Values

n = 1, 2, 3, … z
l = 0, 1, 2, 3, … (z-1)
m l = 0, ±1, ±2, ±3, … ±(z-1)
m s = ±1/2

Summary of Quantum Numbers

Electron Clouds

Multi-electron atoms, Pauli principle, and the periodic table

Band Structure

Hydrogen molecule and molecular bonding

Energy band formation; metals, semiconductors and insulators


Energy Bands

Fermi Energy

need more but confusing tho

Effective mass

Electrons and holes

Intrinsic Semiconductor

Carrier Generation



Doping, extrinsic semiconductors

n-type doping

p-type doping

Carrier concentration

Density of States

Fermi function

$$ f(E) = \frac{1}{1 + e^{\frac{E - E_F}{kT}}} $$
- Fermi-Dirac distribution function gives us the probability that an available energy state at E will be occupied by an electron at temperature T
- probability that an available energy state will be occupied by a hole is 1 - f(E)
- at E=E F , f(E) = 1/2
- E F in intrinsic material: middle of band gap b/c concentration of holes in VB = concentration of electrons in CB
- E F in n-type material: closer to E C because the concentration of electrons in CB is higher than concentration of holes in VB
- E F in p-type material: close to E V because concentration of holes in VB is higher than concentration of electrons in CB

Equilibrium Carrier Concentration

Mass Action Law

$$ n_0 p_0 = n_i^2 \\ n_0 = n_i e^{\frac{E_F - E_i}{kT}} \\ p_0 = n_i e^{\frac{E_i - E_F}{kT}} $$

Conductivity and mobility

Hall Effect

Haynes-Shockley Experiment

Temperature dependence of carrier concentration

$$ n_i (T) = 2{\frac{2\pi kT}{h^2}}^{\frac{3}{2}}{m_n^* m_p^*}^{\frac{3}{4}}e^{\frac{-E_G}{2kT}} $$

Compensation doping

Diffusion Current

need more

Direction and indirect bandgap semiconductors


Energy-band diagrams and MOSFET

MOSFET Operation Modes

MOSFET Band Diagrams


Critical issues with metallization

Metallic bonding

Electrons in metals

Temperature dependence of resistivity

In the Presence of an Electric Field

Drift Velocity


Structural dependence of resistivity


The Meissner Effect

Optical Properties

Light wave propagation, Refraction Index

Refraction Index


Snell’s Law, Total Internal Refraction

Optical Fibers

Photon interaction with materials. Absorption, Reflection, Transmission, Refraction

-from conservation of light, I 0 = I T + I A + I R ,
- I 0 is the intensity of incident light, I T , I A , I R are intensity of transmitted, absorbed, and reflected light
- three types of light-material interactions:
- transmission
- absorption
- reflection
- materials divided into:
- transparent (little absorption and reflection)
- translucent (light scattered within material)
- opaque (relatively little transmission)
- if material not perfectly transparent, light intensity decreases exponentially with distance
- if the light intensity drop in δx is δI δI = -α δx I
- α = absorption co-efficient (m -1 )

Bouger-Lambert-Beer’s Law

$$ ax = -ln(frac{I}{I_0}) $$
- light could be absorbed by the nuclei (all materials) or by the electrons (metals and narrow E g semiconductors)

Atomic Absorption

Absorption in Metals

Absorption in Non-Metals




Emission. Luminescene and Fluroscence

Emission in Non-Metals - Luminescence



Dielectric Materials

Surface Charge and Surface Electricity

Surface Charging

Coulomb’s Law

Capacitance Effects: Fringing Fields

Polarization and Relative Permittivity

What Happens: Dielectric Between Plates of a Capacitor


Polarization Mechanisms

Electrical Polarizability

Molecular Polarizability

Interfacial Polarizability

Frequency Dependence of Polarization

Classification of Dielectrics

AC Permittivity and Dielectric Loss

Gauss’ Law and Boundary Conditions

Dielectric Breakdown

Breakdown Mechanisms

Capacitors and Memories


Piezoelectric Materials

Thermal Properties of Materials

Heat Issues in ICs

Mechansms of Heat Generation and Loss

Overview of Heat

Heat capacity

Dulong-Petit Law

Thermal Conductivity

Classical treatment of heat capacity

$$ C_V = \frac{\partial E}{\partial T} = 3kN_o $$
- classical treatment works well at high temperatures
- implies that heat capacity is constant and independent of temperature
- however, heat capacity is dependent on temperature
- Debye Temperature (θ D ) : temperature at which C V has reached 96% of its final value

Quantum Theory of Heat Capacity

Quantum treatment of thermal conductivity

Classical theory of Thermal Conductivity

- λ is the mean free path between collisions with the lattice
- the idea is that an electron must have undergone a collision in this space and hence will have the energy/temperature of this location

Wiedemann-Franz Law

$$ \frac{K}{\sigma T} = \frac{\pi 2 k 2}{3q^2} = L $$
- L = Lorentz number
- works quite well for metals, but not for “phonon materials”

Thermal resistance

Magnetic Properties

Basic Concepts

Faraday’s Experiment

Para- and Dia-magnetics

Paramagnetic and Ferromagnetics:
$$ B = \nu H = \nu_0 (H + M) $$

- M opposes H
$$ B = \nu H = \nu_0 (H - M) $$

Magnetic Moments

Size of Atomic Magnetic Moment

Bohr Magneton

Alignment of Magnetic Moments in a Solid


Ferro-, Antiferro- and Ferrimagnetism





Curie Temperature

Domains and Hysteresis

The B-H Curve

- as H increases, B follows the path O P Q R
- at R, B value saturates at B s
- B s corresponds to complete alignment of atomic moments
- if the applied field is now reduced after increasing to R, the path follows a different direction
- at H =0, B = B r , known as remanence
- material now has a “permanent” magnetic flux density, becoming a permanent magnet
- to turn B to zero, apply a reverse field
- H c = coercive field or coercivity
- if we further increase B in the reverse direction, get saturation at -B s again
- hysteresis: the different behaviour of the B-H curve for different directions of H, and this curve is called the hysteresis loop

Hard and Soft Materials


Domains in Polycrystals

Magnetic Recording