Semiconductors

In isolated atoms, electrons occupy discrete, well-defined energy levels. However, when atoms come together to form a crystalline solid, their outer electron shells overlap. This interaction splits the discrete energy levels into closely spaced energy bands. The electrical conductivity of any solid is determined by the structure of these bands and how electrons fill them.

Valence Band (VB)

The energy band containing the valence electrons responsible for chemical bonding. At absolute zero (0 K), this band is completely filled with electrons.

Conduction Band (CB)

The higher-energy band where electrons are free to move throughout the crystal lattice, facilitating electrical conduction. At absolute zero, this band is completely empty in insulators and semiconductors.

Forbidden Energy Gap (E_g)

The energy separation between the top of the valence band and the bottom of the conduction band. No electron can possess an energy value falling within this gap.

Classification Based on Band Gap

• Conductors: The valence and conduction bands overlap (E_g ≈ 0 eV), allowing valence electrons to transition into the conduction band with minimal thermal energy.
• Insulators: A very wide energy gap (E_g > 3 eV). It is virtually impossible for an electron to bridge this gap under standard conditions.
• Semiconductors: A narrow energy gap (E_g ≈ 1 eV). At 0 K, they behave as perfect insulators, but at room temperature, thermal energy is sufficient to excite a small fraction of electrons across the gap.

Intrinsic Semiconductors

Intrinsic semiconductors are pure, elemental semiconductor crystals without any deliberate impurities. The most widely used elemental semiconductors are Silicon (Si) (E_g = 1.1 eV) and Germanium (Ge) (E_g = 0.7 eV), both belonging to Group 14 of the periodic table and possessing four valence electrons.

Conduction Mechanism and “Holes”

In a pure silicon crystal, each atom forms four covalent bonds with its neighbors. At room temperature, thermal vibrations occasionally break a covalent bond, releasing a free electron into the conduction band. The departure of an electron leaves behind a vacant space in the covalent bond within the valence band. This vacancy behaves as a virtual particle with a positive charge (+e) and is called a hole. Conduction in semiconductors is unique because it occurs through the simultaneous movement of both negative free electrons in the conduction band and positive holes in the valence band.

Charge Carrier Equilibrium

In an intrinsic semiconductor, free electrons and holes are always generated in pairs. Therefore, the electron concentration (n_e) is strictly equal to the hole concentration (n_h), both matching the intrinsic carrier concentration (n_i):

Effect of Temperature on Conductivity

• At Absolute Zero (0 K): All covalent bonds are perfectly intact. No free carriers exist, so the semiconductor acts as a perfect insulator.
• As Temperature Increases: More covalent bonds break, exponentially increasing the concentration of free electrons and holes. Consequently, the electrical resistance of a semiconductor decreases as temperature rises. This gives semiconductors a Negative Temperature Coefficient of Resistance, contrasting sharply with metals (conductors), whose resistance increases with temperature due to lattice scattering.

Extrinsic Semiconductors (Doping)

Because the electrical conductivity of intrinsic semiconductors is very low at room temperature, it is altered for practical devices through doping. Doping is the deliberate addition of a minute quantity of specific impurity atoms (dopants) to a pure semiconductor crystal, drastically increasing its carrier concentration. Extrinsic semiconductors are categorized into two types depending on the choice of dopant.

N-Type Semiconductors

• Dopant Material: Pentavalent elements from Group 15 of the periodic table, possessing five valence electrons (e.g., Phosphorus (P), Arsenic (As), Antimony (Sb)).
• Mechanism: When a pentavalent atom replaces a silicon atom in the crystal lattice, four of its valence electrons form covalent bonds with adjacent silicon atoms. The fifth valence electron remains loosely bound and is easily donated to the conduction band by ambient thermal energy. These impurities are called Donor impurities.
• Carrier Concentration: Because each dopant atom contributes a free electron without creating a corresponding hole, the concentration of electrons far exceeds that of holes.
  • Majority Carriers: Electrons (n_e \gg n_h)
  • Minority Carriers: Holes
• Charge Neutrality: Although electrons are the majority carriers, the complete n-type crystal remains electrically neutral, because the charge of the free electrons is perfectly balanced by the positive ions left behind at the dopant atom sites.

P-Type Semiconductors

• Dopant Material: Trivalent elements from Group 13 of the periodic table, possessing three valence electrons (e.g., Boron (B), Aluminum (Al), Indium (In), Gallium (Ga)).
• Mechanism: When a trivalent atom replaces a silicon atom, its three valence electrons form bonds with three neighboring silicon atoms. The bond with the fourth neighbor remains incomplete, creating a natural vacancy or hole in the valence band. These impurities are called Acceptor impurities because they readily accept electrons from neighboring bonds.
• Carrier Concentration: Each dopant atom creates a hole without generating a free electron.
  • Majority Carriers: Holes (n_h \gg n_e)
  • Minority Carriers: Electrons
• Charge Neutrality: The p-type crystal remains electrically neutral, as the excess positive holes are balanced by the fixed negative ions created at the acceptor atom sites.

Mass-Action Law

Regardless of the doping type or concentration, a fundamental thermodynamic equilibrium relation holds true for any semiconductor at a constant temperature:

The P-N Junction and Semiconductor Devices

When a p-type semiconductor crystal is seamlessly joined to an n-type semiconductor crystal at an atomic level, a p-n junction is formed. This structure forms the foundation of nearly all solid-state electronics.

Formation of the Depletion Region

• Diffusion: At the interface, free electrons from the n-side naturally diffuse across the junction into the p-side to recombine with holes. Similarly, holes from the p-side diffuse toward the n-side.
• Fixed Ions: As electrons leave the n-side, they leave behind uncompensated, fixed positive donor ions. As holes leave the p-side, they leave behind fixed negative acceptor ions.
• Barrier Potential: These fixed immobile ions accumulate near the junction, creating a region completely devoid of mobile charge carriers called the depletion region. The separation of these charges generates an internal electric field (barrier potential, V_b ≈ 0.7 V for Silicon) that halts any further spontaneous diffusion of majority carriers.

Biasing a P-N Junction (Diode)

Biasing refers to applying an external voltage across the p-n junction to alter its electrical properties.

• Forward Biasing: The positive terminal of an external battery is connected to the p-side, and the negative terminal to the n-side. This external field opposes the internal barrier potential, narrowing the depletion region and allowing a large electric current to flow easily across the junction once the barrier voltage is exceeded.
• Reverse Biasing: The positive terminal is connected to the n-side, and the negative terminal to the p-side. This reinforces the internal barrier potential, widening the depletion region and preventing majority carrier current. Only a microscopic, temperature-dependent reverse saturation current flows due to minority carriers. Thus, a p-n junction diode acts as a one-way electrical valve.

Summary Table of Semiconductor Components and Applications

Modern electronics leverages variations of the basic p-n junction to manipulate light, energy, and electrical signals.