ECE 209 Midterm Notes

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