# MNS321 - Summary
[TOC]
## Comparisons
### **Forward** Bias / **Reverse** Bias?
The ideal flow is electrons flowing from `n->metal->p`.
**Forward bias** facilitates this flow:
For a PN junction, it also decreases the potential difference between bulk regions (`V_bi - V_a`).
- P region connects to [+] electrode. (Fermi level decreases)
- N region connects to [-] electrode. (Fermi level increases)
**Reverse bias** impedes this flow:
For a PN junction, it also increases the potential difference between bulk regions (`V_bi + V_a`).
- N region connects to [+] electrode. (Fermi level decreases)
- P region connects to [-] electrode. (Fermi level increases)
### **Avalanche** Breakdown / **Tunneling** Breakdown?
**Breakdown voltage** (large reverse current):
1. via **avalanche multiplication**: due to electrons acquiring sufficient kinetic energy.
Therefore depends on the electric field.
2. via **tunneling effect** (Zener effect): due to quantum mechanical tunneling of carriers through the bandgap.
Smaller depletion depths enable tunneling.
Tunneling won't contribute much breakdown. AVALANCHE DOES.
### The waveguides in **heterojunction** / **homojunction** that facilitates LASER generation?
- In a **heterojunction**, the interfaces between p-intrinsic and intrinsic-n are reflecting beams that is not going in the transverse direction, thus the structure acts as a weaveguide.
- In a **homojunction**, the crystal planes act as waveguide. Difficult to find right direction/difficult to find a perfect crystal.
### **rectifying** junction / **ohmic** junction?
- The semiconductor work function is smaller than the metal workfunction then it's **rectifying**.
- The semiconductor work function is larger than the metal workfunction then it's **ohmic**.
### **Brillouin** approach / **Bloch** approach?
- **Brillouin**: look at free electron; increase potential; see how `E(k)` gets perturbed.
- **Bloch**: put electrons close to form bonds; see how they overlaps.
## What are those energy levels mentioned in this course?
### Each material is usually characterized by these 3 levels
- The **vacuum level**: the energy of a free stationary electron that is outside of any material (it is in a perfect vacuum).
- The **conduction level**: the lower boundary of the conduction band.
- The **valent level**: the higher boundary of the valent band.
### The Fermi level has different meanings in metal and in semiconductors
For a metal, **Fermi level** is the half-filled energy level.
For a semiconductor, **Fermi level** tells the electorn and hole concentration distributions, in terms of those in the conduction band and the valence band.
$$
n=N_ee^{-\frac{E_c-E_F}{k_BT}}\\p=N_ve^{-\frac{E_F-E_v}{k_BT}}
$$
ちなみに, in the dynamics condition (in the depletion region, where the `E_F` is splitted into 2 curves, namely `F_n` at top and `F_p` at bottom):
$$
n=N_ee^{-\frac{E_c-F_n}{k_BT}}\\p=N_ve^{-\frac{F_p-E_v}{k_BT}}
$$
### Different types of doping result in different types of inserted energy levels
- acceptor level
- donor level
## Definitions
- **Effective Mass**: We do not want to discuss the lattice potential’s effect on the electron, so we bury its real effects by giving the electrons an effective mass.
- **Haynes–Shockley experiment**: The experiment that measures minority carrier concentration.
- **Work function** (energy): Energy required to excite an electron. i.e., the difference between vacuum level and Fermi level.
$$
\phi=E_\text{vacuum}-E_F
$$
- **Contact Potential** (voltage): The potential that carriers feel when 2 different materials come into contact.
$$
V_{CD}=\frac{\phi_1-\phi_2}e
$$
- **Electrochemical potential** (Energy): what actually goes to equilibrium when 2 materials come into contact.
$$
\mu=\phi_1+E_{F,1}=\phi_2+E_{F, 2}
$$
- **Peltier Effect**: heat is emitted or absorbed when an electric current passes across a junction between two materials.
- If e- goes from high Fermi level to low, lattice cools down.
- If e- goes from low Fermi level to high, lattice heats up.
- **Depletion region** / Space charge / barrier region: an insulating region formed by removing *all* free charge carriers from a conducting region.
- **Law of Mass Action** (semiconductor): `Majority carrier concentration * minority carrier concentration = intrinsic carrier concentration ^ 2`:
$$
n\cdot p=n_i^2
$$
- **Exciton**
- **Schottky junction**: metal-semiconductor junction.
- **Built-in potential** (voltage): When a PN junction is in equilibrium, the bulk regions maintain a voltage difference. It is temperature-dependent, and it's determined by all kinds of carrier concentrations:
$$
V_{bi}=\frac{k_bT}e\ln\frac{N_dN_a}{N_i^2}
$$
- **Population inversion**: e- and hole numbers being different from those in the thermodynamic equilibrium state.
- **Complementary metal–oxide–semiconductor** (**CMOS**): uses pMOSFET and nMOSFET.