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Semiconductor physics Cheat Sheet by

This is the cheat sheet for Semiconductor Physics

Introd­uction

Semico­ndu­ctors are 4th group of elements in periodic table.
valence electrons are 4.
ex: Carbon, Silicon, german­ium­,Ti­n,lead.
Mostly used semico­nductor material is Silicon and germanium.
semico­ndu­ctors are negative temper­ature coeffi­cient as the temper­ature increases Energy gap of the semico­nductor decreases.

Intrinsic Semico­ndu­ctors

An intrinsic semico­nductor is a semico­nductor in which no other material is intent­ionally doped (similar to mixing). Example: Si, Ge.
Notes:
1. It behaves as an insulator at absolute zero.
2. Electrons are excited by thermal energy.
3. They are different from pure semico­ndu­ctors and may consist of some level of impuri­ties. The conduc­tivity of intrinsic semico­nductor is more than that of a pure semico­nductor as the impurities provide a few energy levels in the bandgap.
Note:
Pure semico­ndu­ctors are semico­ndu­ctors that have no impuri­ties. Ideally, no semico­nductor is pure in nature.

Mass Action Law

Law of mass action

The law of mass action states that the product of number of electrons in the conduction band and the number of holes in the valence band is constant at a fixed temper­ature and is indepe­ndent of amount of donor and acceptor impurity added.

Mathem­ati­cally it is repres­ented as
np = ni2 = constant
Where ni is the intrinsic carrier concen­tration
n is number of electrons in conduction band
p is number of holes in valence band

Mobility

The charge carriers move by the influence of an external electric field. So, due to the applic­ation of an electric field charge carriers will get some drift velocity to move in the conductors or the Semico­ndu­ctors. Electrical mobility of charge carriers is defined as the drift velocity of the carriers per unit applied electric field.

Now, what is the electron mobility formula? Let, after applying an external electric field E, the charge carriers get the drift velocity V. Then the formula for the mobility of the charge carriers is,

μ= V/E

This is the formula of mobility of charge carriers. This is also the the electron mobility formula.

Classi­fic­ation of Semico­ndu­ctors

There are mainly 2 types of semico­ndu­ctors
1) Intrinsic Semico­ndu­ctors.
2) Extrinsic Semico­ndu­ctors are of 2 types.
1) P-Type Semico­ndu­ctor.
2) N-Type Semico­ndu­ctor.
Semico­nductor contains electrons and holes.

Extrinsic Semico­ndu­ctors

Process of doping
Doping a semico­nductor can be done in many ways including adding impurity to molten semico­ndu­ctor, heating semico­nductor in an atmosphere containing dopant atoms and bombarding semico­nductor with the dopant atoms.

Types of dopants
There are two types of dopants that can be added to a semico­ndu­ctor. This gives rise to the following types of extrinsic semico­ndu­ctors:
1. n-type semico­ndu­ctor: Pentav­alent impurities (Ex: As, P) are added which introduces an extra valence electron which requires lesser energy for conduc­tion. Addition of pentav­alent impurity adds a new energy level (called donor levels) near the conduction band in the energy band diagram.
2. p-type semico­ndu­ctor: Trivalent impurities (Ex: B, In) are added which introduces an extra hole which requires lesser energy for conduc­tion. Addition of trivalent impurity adds a new energy level (called acceptor levels) near the valence band in the energy band diagram.

Charge Neutrality

A semico­nductor is said to be "­Ele­ctrical neutra­l" when the total positive charge concen­tration is equal to total negative charge concen­tration

Types of Materials

CONDUCTORS
Contains plenty of free electrons.
Energy gap = 0.
Semi-C­ond­uctors
Contains Valency Electrons = 4.
Energy gap = 1eV.
Insulators
Tightly bound electrons.
Energy gap >6eV.

Einstein Relati­onship (semic­ond­uctor)

The equation which relates the mobility µ (of electrons or holes) and the diffusion coeffi­cient (of electrons Dn or holes Dp) is known as Einstein Relati­onship.
 

Hall Effect

Principle of Hall Effect

The principle of Hall Effect states that when a curren­t-c­arrying conductor or a semico­nductor is introduced to a perpen­dicular magnetic field, a voltage can be measured at the right angle to the current path. This effect of obtaining a measurable voltage is known as the Hall Effect.

The Hall voltage repres­ented as VH is given by the formula:
V(hall effect) = IB / qnd

Here,
I is the current flowing through the sensor
B is the magnetic Field Strength
q is the charge
n is the number of charge carriers per unit volume
d is the thickness of the sensor.
 

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