Semiconductor Classifications

Materials can be classified based on their conductivity as conductors (high conductivity, low resistivity), insulators (low conductivity, high resistivity), or semiconductors (intermediate conductivity and resistivity).

From an energy band perspective, conductors have overlapping valence and conduction bands, allowing electrons to move freely. Insulators have a wide gap between bands, preventing electron movement. Semiconductors like silicon and germanium have a moderate energy gap of about 3 eV between bands.

In silicon and germanium crystals (both with 4 valence electrons), the energy states form two main bands. The valence band contains the 4N electrons from N atoms, while the conduction band sits above it, empty at low temperatures.

💡 Think of energy bands like apartment buildings - the valence band is the lower floors where electrons normally live, while the conduction band is the upper floors they can move to when given enough energy!

Intrinsic Semiconductors

An intrinsic semiconductor is pure and conducts better as temperature increases. At absolute zero, it behaves like an insulator, but as temperature rises, thermal energy breaks some covalent bonds, creating free electrons and holes (electron vacancies with positive charge).

The number of free electrons equals the number of holes, known as the intrinsic carrier concentration $n₁ = nₑ = nₕ$. These carriers generate current when an electric field is applied, with total current being the sum of electron and hole currents $I = Iₑ + Iₕ$.

In a semiconductor, two processes happen simultaneously: generation of electron-hole pairs and recombination (when free electrons fill holes). At equilibrium, these rates are equal. Different semiconductors require different amounts of energy to free electrons - germanium needs less than silicon, so it has more free electrons at the same temperature.

💡 The balance between generation and recombination of electron-hole pairs is like a busy parking lot - cars are constantly arriving and leaving, but the total number stays roughly the same in equilibrium!

Extrinsic Semiconductors

Extrinsic semiconductors are created through doping - adding specific impurities to improve conductivity. There are two main types:

When a trivalent impurity (with 3 valence electrons) is added to silicon or germanium, a p-type semiconductor forms. The impurity creates holes because it's missing an electron to complete all covalent bonds. Holes become the majority carriers, vastly outnumbering electrons.

Adding a pentavalent impurity (with 5 valence electrons) creates an n-type semiconductor. Four electrons form bonds while the fifth electron is loosely attached and easily becomes free. Here, electrons are the majority carriers, greatly outnumbering holes.

Despite having excess carriers, the crystal remains electrically neutral overall - the charge of the added carriers is balanced by the oppositely charged impurity atoms. At thermal equilibrium, the product of electron and hole concentrations equals the square of the intrinsic carrier concentration $nₑnₕ = n₁²$.

💡 Doping is like adding ringers to a sports team - a few strategic additions (impurity atoms) can dramatically change how the whole team (semiconductor) performs!

P-N Junction Formation

When p-type and n-type semiconductors join, a p-n junction forms. Initially, holes from the p-side diffuse toward the n-side, and electrons from the n-side diffuse toward the p-side. This movement creates a diffusion current.

As carriers move across the junction, they leave behind charged ions, creating a depletion region about 0.1 micrometers thick. The n-side becomes positively charged (from donor ions) and the p-side becomes negatively charged (from acceptor ions). This charge separation creates an electric field from the n-side to p-side.

This electric field causes a drift current in the opposite direction of the diffusion current. Electrons move from p-side to n-side, and holes move from n-side to p-side. At equilibrium, drift current exactly balances diffusion current, resulting in no net current flow.

The potential difference across the junction is called barrier potential. It prevents further electron movement from n-side to p-side, maintaining equilibrium without an external voltage.

💡 The depletion region works like a border checkpoint - it develops naturally to control the flow of charge carriers and maintain order in the semiconductor!

P-N Junction Under Bias

In forward bias, the p-side connects to the positive terminal and the n-side to the negative terminal of a voltage source. This setup opposes the barrier potential, reducing the barrier height to $Vo - V$, where Vo is the original barrier potential.

Forward bias causes minority carrier injection - electrons move from n-side to p-side and holes from p-side to n-side across the depletion layer. The concentration of these carriers is highest at the junction edge. Current flows as they move through the semiconductor, typically measured in milliamps (mA). The current increases significantly after reaching the threshold voltage.

In reverse bias, connections are swapped - the n-side connects to positive and p-side to negative. This increases the barrier height to $Vo + V$, strengthening the barrier. Diffusion current decreases dramatically, resulting in minimal current flow (measured in microamps, μA) until reaching the breakdown voltage, where current suddenly increases sharply.

💡 Forward bias is like opening a dam gate - it reduces the barrier and lets charge carriers flow freely. Reverse bias does the opposite, building the barrier higher and blocking most current!

Semiconductor Applications

The difference between forward and reverse bias resistance is key to rectification - converting AC to DC. Since a diode allows current in only one direction, it can filter an AC signal:

A half-wave rectifier uses one diode, producing output voltage only during forward-biased half-cycles. This gives half of the input AC wave as output, wasting half the potential power.

A full-wave rectifier uses two diodes to utilize both positive and negative halves of the AC wave. This makes it more efficient than a half-wave rectifier, providing power during both halves of the input cycle.

The diode's dynamic resistance $r = ΔV/ΔI$ varies between forward and reverse bias conditions. This property is crucial for designing semiconductor circuits with predictable behaviors.

💡 Rectifiers are like one-way valves for electricity - they ensure current flows only in the desired direction, turning alternating current (AC) into direct current (DC) that powers most of our electronic devices!