Summary and Terms

Terms

Electric Field: A field which charged particles feel based on nearby charges or moving magnets. The force a particle feels $F$ in a given electric field $\mathcal{E}$ is given by $q\mathcal{E}$ where $q$ is the charge of a given particle. Note that both $F$ and $\mathcal{E}$ are vectors. Section 13.3.2

Voltage: A measure of the potential energy a particle has within a given electric field normalized to the charge of the particle. Voltage $V$ in an electric field $\mathcal{E}$ is given by $\mathcal{E}L$ where $L$ is some distance the charge will move through, analogous to height in a gravitational field. Section 13.3.3

Current: The rate of flow of charge through a wire, or the number of charges that pass per second, represented by $I$. Section 13.3.4

Resistance: The proportionality between voltage and current as in Ohm's Law: $V = IR$. The reciprocal of Resistance is the conductance $G$. Importantly, resistance is dependent on the geometry of the specimen. Section 13.3.4

Free Electron Model: A model in which we assume electrons are completely free to move around in a material, which is true in metals and a some other materials. Section 13.4.1

Resistivity: A geometry-independent metric $\rho$ for how much a material resists the flow of current. Resistivity is related to resistance by: $\rho= \frac{RA}{\ell}$ Where $A$ is the cross-sectional area of the wire and $\ell$ is the length of the wire. Conductivity $\sigma$ is the reciprocal of resistivity. Section 13.5.1

Resonance Structures: Equivalent arrangements of electrons which a molecule "resonates" between. Resonance structures which do not preserve charge balance are called "synchronized"resonance structures. Section 13.6.3

Delocalized Electrons: Electrons which participate in bonding with more than one atom via resonance. Section 13.6.4

Electron Scattering: When an electron moves through a crystal and bumps into something, usually some kind of defect, which can change the direction the electron is moving and its speed. Section 13.7.1

Phonons: Fluctuations or vibrations in a material which propagate through a material as waves. Phonons increase in intensity and number as a crystal is heated, cause oscillations in the electron density of the material, and act as scatterers to moving electrons. Section 13.7.3

Defect Scattering: Because defects change the local electronic bonding environment within a material, they can act as scattering sites. Section 13.8.1

Drift Velocity: The average velocity of electrons moving in a material, usually under some applied electric field. Section 13.8.2

Electron Mobility: The proportionality constant between the drift velocity $v_d$ and the applied field $\mathcal{E}$, denoted $\mu_e$.

$$ v_d = \mu_e \mathcal{E} $$

Mobility is inversely proportional to the frequency of scattering events $f_s$. $$\mu_e \propto \frac{1}{f_s}$$. Section 13.8.2

Conductivity: A material's conductivity is given by: $$\sigma = n |e| \mu_e$$

Where:

$n$ = the volumetric density or concentration of free electrons

$e$ = the charge of a single electron

$\mu_e$ = the mobility of electrons within the material

Section 13.8.4

Semiconductors: Materials which, unusually, increase in conductivity as their temperature increases. This effect is due to an increase in available charge carriers as electrons are promoted to higher-energy electronic states (across the band gap) in greater numbers. Section 13.9.1

Band Theory: a model which groups all a material's electronic states into bands of allowed energies rather than distinct orbitals. The most important of these bands are the valence band, the highest energy band with electrons present, and the conduction band, the lowest energy band without electrons present.

In band theory, conductors can conduct due to empty spaces in their valence bands which electrons can use to move around. Semiconductors conduct by promoting electrons from the valence band into the conduction band, where they are also free to move around. Section 13.9.6

Band Gap: The energy difference between the top of the valence band and the bottom of the conduction band. This is the minimum energy required to promote a valence electron into the conduction band. Section 13.10.1

Holes: Charge carriers that represent the absence of an electron and carry a positive charge. Holes typically have distinct drift velocities $v_h$, concentrations $p$ and mobilities $\mu_h$ from electrons. Question 13.10.1.3

Doping: The process of adding impurity atoms with different electronic properties to a semiconductor. Doping is used to create extrinsic semiconductors. Section 13.11.1

p-type Semiconductor: A semiconductor which has been doped with an atom that has fewer valence electrons than the host lattice, causing one or more electrons to be bound to the dopant and freeing a hold for conduction. Section 13.11.1

n-type Semiconductor: A semiconductor which has been doped with an atom that has more valence electrons than the host lattice, causing one or more electrons to be donated to the host lattice where they can conduct. Section 13.11.1

In both p- and n-type semiconductors, the lattice remains charge-neutral.

pn-junction: A junction created by contacting a p-type and n-type semiconductor which causes a built in voltage to form. pn junctions are the foundation of MOSFETs, which are incredibly useful. Section 13.12.1

MOSFET: Metal-Organic-Semiconductor Field-Effect Transistors are devices which can either be conductive or insulating based on some input signal. MOSFETs are the basis of logic gates and all modern computing. Section 13.12.4