SEMICONDUCTORS

Definition of Semiconductor:
- A semiconductor is a material that has an electrical conductivity between that of a conductor and an insulator.
Key Requirement for Semiconductor:
- An element must have 4 electrons (e⁻) in its outermost shell to be considered a semiconductor.
Stability Requirement:
Atoms strive for stability by achieving 8 electrons in their outer shell, known as the octet rule. Silicon (Si), with 4 outer electrons, aims to gain 4 additional electrons for this stable configuration.
- Silicon (Si), having 4 electrons in its outer shell, seeks to acquire 4 more electrons to reach this stable configuration.

Covalent Bond Formation:
- When silicon atoms are in close proximity, they share their outermost electrons, forming covalent bonds.
- This allows silicon atoms to effectively achieve an octet, resulting in a stable structure.
Pure or Intrinsic Semiconductor:
- In a pure semiconductor, the outermost electrons are engaged in forming covalent bonds.
- Electric Conductivity:
- Without external energy, the electrons remain bound within these bonds, preventing electric current conduction.
- At lower temperatures, semiconductors behave as insulators.

Impact of Temperature:
- When temperature is increased, the covalent bonds break, causing some outer electrons to become free electrons.
- This event allows current conduction when there is an external electric potential.
Statistics of Free Electrons:
- At room temperature (300K), intrinsic silicon has 1.5 x 10¹⁰ free electrons per cubic centimeter (n_i).

Bound vs. Free Electrons:
- At low temperatures, nearly all outermost electrons in semiconductor materials participate in covalent bonds, referred to as bound electrons.
- Valence Band:
- The energy level occupied by bound electrons is termed the Valence Band.
Behavior at Higher Temperatures:
- As bound electrons absorb energy (e.g., from heat), they vibrate, break covalent bonds, and can jump to a higher energy state known as the Conduction Band.
- When this happens, a vacancy is created in the valence band, known as a hole.
Energy Gap ( extit{E_g}):
- The difference in energy levels between the valence band and conduction band is termed the energy gap:
- For a semiconductor, this is typically around 0.67 eV for Germanium (Ge).
- For insulators, the energy gap is typically greater than 5 eV, while for metallic conductors, it approaches 0 eV.

Equation for Carrier Concentration:
- The concentration of free electrons (n) in pure silicon at room temperature is expressed as:
- $n_i = 1.5 x 10^{10} ext{ cm}^{-3}$
- The same concentration is also applicable for holes (p).

Purpose of Doping:
- To enhance the conductivity of intrinsic semiconductors, impurity atoms are introduced through a process known as doping.
Types of Doping:
- N-Type Doping:
- Involves adding pentavalent impurities (e.g., Phosphorus (P)). This generates an excess of free electrons.
- P-Type Doping:
- Involves adding trivalent impurities (e.g., Boron (B)). This creates an excess of holes (missing electrons).

Majority and Minority Carriers:
- In an n-type semiconductor, the excess free electrons are termed majority carriers, and holes are the minority carriers.
- For example, if the inherent carrier concentration in pure Si is:
- $n = p = 1.5 x 10^{10} ext{ cm}^{-3}$
- Adding pentavalent impurities with concentration N_d = 2 x 10^{20} will result in a new electron concentration:
- $n = ni + Nd = (1.5 x 10^{10} + 2 x 10^{20}) ext{ cm}^{-3}$
- Thus, the majority carrier concentration greatly exceeds that of the minority carriers.
Law of Mass Action:
- States that $n imes p = n_i^2$ where:
- -n = electron concentration
- -p = hole concentration
- -n_i = intrinsic carrier concentration.

Carrier Concentration:
- In a p-type semiconductor, due to the addition of trivalent impurities, for example Boron, there will be an excess of holes, defined as:majority carriers while electrons are termed the minority carriers.

Basic Concept:
- A p-n junction is created when p-type and n-type materials are joined.
Junction Behavior:
- When formed, majority carriers diffuse across the junction region due to a concentration gradient.
- As electrons and holes meet, they recombine, forming a depletion region that is permeated by immobile ions only, with an established electric field.

Depletion Region:
- An area devoid of any mobile charge carriers, solely occupied by immobile ions, creating an electric field.
- Barrier Potential (V_bi):
- An intrinsic potential created across the p-n junction, typically expressed as: $V{bi} = VT ext{ In} rac{NA ND}{n_i^2}$ where:
 - $V_T$ is the thermal voltage (approximately 26mV at room temperature).

Forward Bias:
- The external voltage reduces the junction barrier, allowing current to flow; characterized by electron and hole flow and potential drop across both sides.
Reverse Bias:
- Applies voltage in the opposite direction, increasing the height of the potential barrier and reducing charge carrier movement across the junction.
Reverse Current Characteristics:
- A small reverse saturation current exists due to minority carriers flowing across the junction even in reverse bias conditions.

Zener Breakdown:
- Occurs in highly doped junctions, where electric fields become sufficiently strong, enabling the breaking of covalent bonds even at low voltages.
Avalanche Breakdown:
- Results from collisions creating more free electrons when reverse bias causes a surge in current; this typically occurs at higher reverse voltages.

Use of Diodes:
- Diodes have various applications in electronic circuits, including clippers, clamps, and voltage regulators.