Semiconductor Physics: Understanding Conductivity and Doping

Semiconductor physics is a cornerstone of modern electronics. Understanding the fundamental properties of materials like insulators, conductors, and semiconductors is crucial for designing and developing electronic devices. This article delves into the basics of semiconductor physics, exploring the characteristics of these materials and the principles governing their behavior.

Materials are generally classified based on their electrical conductivity. Insulators offer very low conductivity, conductors offer high conductivity, and semiconductors fall in between. Insulators like paper and glass have high resistivity (10^10 to 10^12 Ω-cm) due to a large energy band gap (>5eV), preventing electron flow. Conductors like copper and aluminum have low resistivity (10^-4 to 10^-6 Ω-cm) because their valence and conduction bands overlap, allowing free electron movement even at absolute zero. Semiconductors, such as silicon and germanium, have intermediate resistivity (10 to 10^4 Ω-cm) and a smaller band gap (around 1eV), enabling conductivity to vary with temperature and doping.

Intrinsic semiconductors are pure forms of semiconductors like silicon (Si) and germanium (Ge). Silicon, with an atomic number of 14, has four valence electrons that form covalent bonds with neighboring atoms in a crystal structure. At absolute zero (0K), these materials act as insulators due to the lack of free electrons. However, at room temperature, thermal energy breaks some covalent bonds, creating free electrons and holes (the absence of electrons). These free electrons and holes contribute to conductivity. In a pure semiconductor, the number of holes equals the number of free electrons.

The conductivity of intrinsic semiconductors is limited. To enhance conductivity, a process called doping is used, where small amounts of impurities are added. This creates extrinsic semiconductors, which are either N-type or P-type, depending on the impurity added. The amount of impurity added is typically 1 part in 10^6 atoms.

N-type semiconductors are created by doping an intrinsic semiconductor with a pentavalent impurity, such as phosphorus or arsenic. These impurities have five valence electrons. Four of these electrons form covalent bonds with the semiconductor atoms, while the fifth electron is loosely bound. This loosely bound electron can easily be excited into the conduction band with minimal energy, increasing the number of free electrons. In N-type semiconductors, electrons are the majority carriers, and holes are the minority carriers. The addition of pentavalent impurities creates a donor energy level just below the conduction band, facilitating electron excitation.

P-type semiconductors are created by doping an intrinsic semiconductor with a trivalent impurity, such as boron or gallium. These impurities have three valence electrons, creating a 'hole' or vacancy in the covalent bond structure. This hole can easily accept an electron from a neighboring atom, effectively creating a positive charge carrier. In P-type semiconductors, holes are the majority carriers, and electrons are the minority carriers. Trivalent impurities act as acceptor atoms, creating a large number of holes in the valence band.

The conductivity of a semiconductor is determined by the number of charge carriers (electrons and holes) and their mobility. In intrinsic semiconductors, the number of electrons and holes are equal. In extrinsic semiconductors, doping significantly alters the carrier concentrations. The conductivity (σ) is given by σ = q(nμn + pμp), where n is the electron concentration, p is the hole concentration, μn is the electron mobility, μp is the hole mobility, and q is the elementary charge. N-type semiconductors have higher electron concentration (n >> p), while P-type semiconductors have higher hole concentration (p >> n). Generally, N-type semiconductors have higher conductivity than P-type semiconductors for the same doping level due to the higher mobility of electrons compared to holes.

A p-n junction is formed by joining a p-type and an n-type semiconductor. At the junction, electrons from the n-side diffuse to the p-side, and holes from the p-side diffuse to the n-side, creating a depletion region. This diffusion establishes an electric field that opposes further diffusion, resulting in an equilibrium state. Applying a forward bias (positive voltage to the p-side) reduces the potential barrier, allowing current to flow. Applying a reverse bias increases the barrier, limiting current flow. The diode current equation describes the relationship between voltage and current in a p-n junction diode, considering factors like minority carrier diffusion and recombination.