Quantum mechanics

advanced mathematics

Some knowledge of college physics

1. Pay attention to boundary conditions and scene constraints

2. Expression

Semiconductor material

solid lattice

Impurities and Defects

Three basic principles

Schrödinger equation

Wave function (note: probability wave)

Free electrons and bound electrons

Single electron: represents: H atom

Polyelectrons: their quantum states are discrete

energy band formation

One-dimensional infinite crystal energy band

carrier

state density function

Fermi-Dirac distribution function

formula

Intrinsic semiconductor: A pure semiconductor that has no other impurities and no lattice defects.

Product of carrier concentration

Intrinsic Fermi level position

Donor impurities: generated due to the introduction of impurities, are called donor electrons, corresponding to the doping of donor impurities.

Acceptor impurity: After doping with other elements, it accepts electrons in the valence band for ionization and generates holes in the valence band.

Electricity Neutrality Condition: All positively charged charge densities present inside a uniformly doped thermally balanced semiconductor are equal to all negatively charged charge densities.

Extrinsic Semiconductor: Doped Semiconductor

Definition: A semiconductor containing both donor and acceptor impurities.

Classification

1. The Fermi level moves to both sides of the forbidden band as the doping concentration increases.

2. The Fermi level also changes with temperature. As the temperature increases, the Fermi level of both N-type and P-type semiconductors moves closer to the center of the forbidden band. This result is consistent with the behavior of semiconductors in the intrinsic excitation region with the highest temperature, because It satisfies 10=po, so the Fermi level also approaches the intrinsic Fermi level, which is the center of the forbidden band.

3. When the Fermi level is located in the center of the forbidden band, it is an intrinsic semiconductor.

carrier concentration

Classification: When the doped impurity concentration is small (compared to Nc, Nv), it is called a non-degenerate semiconductor. When the doped impurity degree is large (larger than Nc, Nv), it is called a degenerate semiconductor. Given that the one between the two is called a weakly degenerate semiconductor.

Bandgap narrowing effect: the lower position of the conduction band is lowered and the bandgap width is narrowed.

scattering

Mobility versus temperature and doping concentration

Resistivity: ρ=1/σ=1/e (Nμn Pμp)

Saturation velocity and strong field mobility

Diffusion: The process by which carriers move from a high concentration area to a low concentration area under the influence of concentration gradient.

Mobility: A quantity that describes the ease with which carriers move under the influence of an external electric field.

Diffusion coefficient: A quantity that describes the ease with which carriers move under the influence of concentration gradients

Einstein's relationship is the relationship between Miao's carrier mobility and diffusion coefficient

definition

production rate and recombination rate

Source: temperature, light, etc.

Factors affecting carrier recombination: electrons, holes, etc.

Generation and recombination of carriers under thermal equilibrium

Carrier recombination under non-equilibrium

continuity equation

diffusion equation

Definition: Excess electrons and excess holes will be closely connected to drift or diffuse together with a single mobility or diffusion coefficient.

bipolar transport equation

Bipolar transport equation under small injection

application

Mutation knot (when the concentration on one side is much greater than the other side - one-sided mutation knot)

linear grade junction

Many children

Young son

Positive and negative ionized impurities have equal charges

Under equilibrium state, the net hole and electron current density is 0 -> Derivation of Vbi

Depletion approximation (carriers completely diffused away) depletion region

neutral approximation neutral zone

The above-derived formulas for balanced PN junctions can be extended to the case where there is an external voltage. If it is assumed that the external voltage all falls on the depletion region, then Vbi in the formula only needs to be replaced by Vbi-V Note: 1. The reference direction of the applied voltage is opposite to Vbi, and V<=Vbi 2. When V approaches Vbi, a large current situation will occur, and the voltage drop in the quasi-neutral region cannot be ignored.

Energy band diagram

Carrier distribution in space charge region

At equilibrium

Forward bias V>0

Reverse bias V<0

Ideal PN junction DC current and voltage characteristics

Barrier region generates recombination current

Calculation of composite current

small injection conditions

Large injection conditions

Large injection current concentration

Self-constructed electric field under large injection

Work functions of metals and semiconductors

Ideal metal-to-semiconductor contact

Ideal semiconductor contact properties

Current-Voltage Relationship

Ohmic contact: When the semiconductor is connected to the positive electrode of the power supply, the amount of energy band bending is reduced, and electrons can easily pass through the potential barrier and flow from the metal to the semiconductor.

Classification

Its energy band diagram

Abrupt inversion heterojunction built-in electric field and space charge region width

mutant homojunction

Current transport model in mutant inversion heterojunction

Current transport model in mutant homoheterojunctions