Energy Bands in Solids: Valence, Conduction & Forbidden Gap

This section covers semiconductor doping in detail. N-type semiconductors are created by adding Group 15 elements (like phosphorus) to germanium. These dopants have 5 valence electrons while germanium has 4, creating an extra free electron that conducts electricity. P-type semiconductors are created by adding Group 13 elements (like boron) to germanium. These dopants have only 3 valence electrons, creating a 'hole' that can accept electrons from neighboring atoms. In n-type materials, free electrons are majority charge carriers (negative charge). In p-type materials, holes are majority charge carriers (positive charge). Current flows in the direction of hole movement, while electrons move in the opposite direction to fill holes.

Doping improves semiconductor conductivity by adding impurities (few parts per million). Pentavalent dopants (As, Sb, P, valency 5) create n-type semiconductors: four electrons bond with neighbors, leaving one weakly bound electron (ionization energy ~0.01-0.05 eV). This electron becomes free for conduction, acting as a donor impurity. Donor energy levels lie slightly below the conduction band. Trivalent dopants (B, Al, In, valency 3) create p-type semiconductors: lacking one electron creates a hole that can accept electrons from neighboring atoms. Acceptor energy levels lie slightly above the valence band. In n-type materials, electrons are majority carriers (nₑ >> nₕ); in p-type materials, holes are majority carriers (nₕ >> nₑ). The crystal maintains charge neutrality as ionized dopant cores balance free carrier charges.

Doping intentionally introduces impurities to modify semiconductor properties. In silicon (a semiconductor with filled valence band, band gap, and empty conduction band), replacing silicon with phosphorus (one step right in periodic table) creates n-type doping: phosphorus has one extra electron that enters the conduction band, while the extra positive charge remains in the lattice. The extra electron becomes a free carrier. Conversely, replacing silicon with boron (one step left) creates p-type doping: boron has one fewer electron, creating an extra hole in the valence band. Elements in the same column (phosphorus, arsenic, nitrogen) behave similarly, while elements on the opposite side (boron, aluminum) create holes. This controlled doping enables creation of p-n junctions and other semiconductor devices.

Doping introduces controlled impurities into pure silicon (99.999% purity) to modify conductivity. N-type semiconductors use pentavalent dopants (phosphorus, antimony) with five valence electrons, creating extra free electrons. P-type semiconductors use trivalent dopants (boron) with three valence electrons, creating holes (positive charge carriers). This controlled doping enables the creation of electronic devices with tailored electrical properties.

Pure semiconductor materials (intrinsic) have limited conductivity that can only be changed by temperature. Doping introduces impurity atoms to dramatically alter electrical properties. N-type semiconductors are created by doping with pentavalent impurities (like phosphorus or arsenic) that have five valence electrons. When these atoms replace silicon atoms in the crystal lattice, four electrons form covalent bonds while the fifth becomes a free electron in the conduction band. These impurities are called donor impurities because they donate electrons. The material remains electrically neutral overall, with electrons as majority carriers. P-type semiconductors are created by doping with trivalent impurities (like boron or aluminum) that have three valence electrons. These atoms create vacancies or holes in the crystal lattice. These impurities are called acceptor impurities because they accept electrons from neighboring atoms. Holes become the majority carriers in P-type materials.

A PN junction is formed when a p-type semiconductor is joined with an n-type semiconductor. This junction is the basis for most semiconductor devices including diodes, transistors, and solar cells. The PN junction creates a region where the properties of both types of semiconductors interact, allowing for controlled electrical behavior.

When p-type and n-type silicon contact, they form a PN junction, the foundation of solid-state electronics. This creates a diode allowing current in one direction only. Near the junction, electrons diffuse into holes, forming a depletion zone that acts as an insulator. This creates electrical imbalance: n-type becomes positive (missing electrons), p-type becomes negative (extra electrons). Under forward bias (negative battery to n-type, positive to p-type), voltage (~7V for silicon) overcomes the depletion zone, enabling current flow. Under reverse bias, charge carriers are pulled away, creating a larger depletion zone and blocking current. These principles enable solar cells (light generates electron-hole pairs in depletion zone) and LEDs (forward-biased electrons combine with holes, emitting photons).

A diode is a semiconductor device that allows current to flow in only one direction due to the p-n junction structure; when p-type silicon (doped with trivalent boron, creating extra holes) is joined with n-type silicon (doped with pentavalent arsenic, creating extra free electrons), electrons diffuse from the n-side to the p-side and holes diffuse in the opposite direction, creating a depletion region with a built-in electrical potential that blocks current flow until sufficient voltage is applied to overcome this barrier.

This section covers p-n junctions and diodes. A p-n junction is formed by dividing a semiconductor crystal and doping one half with N-type and the other with P-type impurities. The depletion region contains positive ions in the n-region and negative ions in the p-region, creating an electric field. The barrier potential prevents further charge movement. Two types of bias exist: forward bias (reduces barrier, allows current flow) and reverse bias (increases barrier, prevents current flow). Types of diodes include: photodiode (light sensor), solar cell (light to electricity converter), LED (light emitter), and rectifier diode (AC to DC converter).

A p-n junction forms when p-type and n-type materials join, creating a depletion region where mobile carriers diffuse and recombine, leaving fixed ions. This region establishes a barrier potential (0.3-0.7V for silicon) opposing further carrier movement. Biasing controls junction behavior: forward bias reduces the depletion region and lowers the barrier, enabling current flow once the cut-off voltage is exceeded; reverse bias widens the depletion region and blocks current. The cut-off voltage represents the minimum forward voltage for significant conduction. Breakdown voltage marks the reverse voltage threshold where avalanche breakdown causes sudden current surge. These characteristics define diode operation and enable rectification, switching, and voltage regulation functions in electronic circuits.

At temperatures above absolute zero, electrons thermally excite across band gaps, creating electron-hole pairs. Holes represent positive charge carriers formed by electron vacancies. Electrons and holes move through lattices via different mechanisms: electrons move freely, while holes move as neighboring electrons fill vacancies. In steady-state, generation rates equal recombination rates. This balance determines carrier concentrations and is fundamental to semiconductor device operation, including diodes and transistors.

A hole is a vacancy created when an electron leaves its position in the valence band, leaving behind a positively charged vacancy. Holes behave as positive charge carriers because when an electron moves to fill a hole, it appears as if the hole moved in the opposite direction. In intrinsic semiconductors, the number of free electrons equals the number of holes. Electrons are negatively charged carriers, while holes are positively charged carriers. This understanding is fundamental to analyzing semiconductor device operation.

In semiconductor physics, when an electron leaves the valence band, it creates a vacancy that behaves like a positive charge carrier called a hole. Although holes are not actual particles, they are treated as positive charge carriers in theoretical models because they respond to electric fields in ways that appear to be positive charges. This concept simplifies the analysis of semiconductor conduction mechanisms.

In semiconductors, electrons can break free from their parent atoms, becoming conduction electrons while leaving behind positively charged vacancies called holes. This process is reversible—free electrons can recombine with holes at neighboring atoms. At thermal equilibrium, the rates of electron-hole pair generation and recombination are balanced, maintaining a constant concentration of charge carriers. When an external electric field is applied, both electrons and holes contribute to current flow, with electrons moving toward positive terminals and holes appearing to move toward negative terminals due to the absence of electrons.

Holes are created when electrons leave their positions in the valence band, creating vacancies that behave as positive charge carriers. When electrons move through the semiconductor, they leave behind holes that move in the opposite direction. This concept is essential for understanding current flow in semiconductors, where both electrons and holes contribute to conductivity.

The band gap determines whether a material can emit light. In gallium arsenide (GaAs), the band gap allows electrons to fall from the conduction band to the valence band while emitting photons (light). The wavelength (color) of emitted light depends on the band gap size - larger gaps produce shorter wavelength (bluer) light. This relationship between band gap and optical properties is fundamental to optoelectronic devices like LEDs and laser diodes. The band gap also determines whether a material conducts electricity.

The energy band gap—the distance between valence and conduction band edges—determines semiconductor optical behavior. When photon energy hν equals or exceeds the band gap, electrons transition between bands, forming the basis for light-emitting diodes. Optical properties are characterized by complex refractive index: the real part determines light propagation velocity/wavelength, while the imaginary part (extinction coefficient) determines absorption coefficient. Near the absorption edge, absorption coefficient follows α ∝ (hν - E_g)^γ, showing that only photons with sufficient energy cause significant absorption. This relationship enables measurement of band gap energies through optical spectroscopy.

Optical emission in materials occurs when electrons are excited across the band gap and then fall back, emitting photons whose energy equals the band gap; this principle enables LEDs and lasers, with blue light being particularly valuable for displays and white LEDs due to its high energy; similarly, optical absorption in photovoltaic materials depends on band gap matching with solar spectrum wavelengths, leading to multi-junction solar cells that combine multiple semiconductor layers with different band gaps to maximize solar energy conversion efficiency.

In solids, atomic energy levels broaden into energy bands. The valence band is filled with electrons, while the conduction band is empty. The gap between them is called the band gap. This determines whether a material is a conductor, semiconductor, or insulator. Semiconductors have a moderate band gap (typically 0.1-3 eV). At room temperature, some electrons can be thermally excited across the band gap, allowing some conductivity. Different LED colors require different semiconductor materials with appropriate band gaps. Red LEDs use materials like indium phosphide, while blue LEDs use gallium nitride alloys. The band gap determines the wavelength of emitted light.

Band gaps can be direct or indirect. In direct transitions, electrons move between states with same crystal momentum, requiring only energy conservation. In indirect transitions, phonon assistance is needed to conserve momentum. Direct transitions are much more probable. Silicon has an indirect band gap (~1.1 eV), making it less efficient for light-emitting devices. Gallium arsenide has a direct band gap (~1.4 eV), making it efficient for LEDs and lasers. The band gap energy determines whether materials are transparent or opaque to visible light.