Understanding Energy Bands and Semiconductor Physics

$\Delta E_g = E_c - E_v$

• Conductors: Have a very small or zero energy gap ($\Delta E_g \simeq 0$), allowing electrons to flow easily.
• Insulators: Possess a very large forbidden gap (typically $> 3 \text{ eV}$), making it nearly impossible for electrons to jump to the conduction band.
• Semiconductors: Have a small energy gap (e.g., Silicon $\approx 1.1 \text{ eV}$, Germanium $\approx 0.7 \text{ eV}$).

Exam Tip: Semiconductors exhibit a unique temperature relationship. Unlike metals, as temperature increases, their conductivity increases and their resistivity decreases because thermal energy helps electrons jump the small gap.

Types of Semiconductors

Semiconductors are categorized based on their purity and how they are manipulated to conduct electricity.

Intrinsic Semiconductors

An intrinsic semiconductor is a pure form of the material (such as pure Silicon or Germanium). In these materials, the number of free electrons ($n_e$) is exactly equal to the number of holes ($n_h$) created by thermal excitation:

$n_e = n_h$

Because the number of charge carriers is relatively low at room temperature, intrinsic semiconductors have limited practical use in electronic devices.

Extrinsic Semiconductors and Doping

To make semiconductors useful, we perform doping—the process of adding specific impurities to the crystal lattice to increase the number of charge carriers. This results in extrinsic semiconductors.

n-type Semiconductors

n-type semiconductors are created by adding Group V elements (such as Phosphorus (P), Arsenic (As), or Antimony (Sb)) to a Group IV element like Silicon. Since Group V atoms have five valence electrons and only four are needed for bonding, one extra electron is provided. These impurities are called donors. In n-type material, electrons are the majority carriers ($n_e > n_h$).

p-type Semiconductors

p-type semiconductors are created by adding Group III elements (such as Boron (B), Aluminum (Al), or Gallium (Ga)) to a Group IV element. These atoms have only three valence electrons, creating a deficiency or "vacancy" in the covalent bond. This vacancy is called a hole, and the impurities are known as acceptors. In p-type material, holes are the majority carriers ($n_h > n_e$).

Charge Carriers and Conductivity

Holes and Electrical Current

In semiconductor physics, a hole is treated as a physical particle with a positive charge. It is essentially the absence of an electron in a covalent bond. When an electric field is applied, holes move in the direction opposite to the flow of electrons. The total electrical current ($I$) in a semiconductor is the sum of the electron current ($I_e$) and the hole current ($I_h$):

$I = I_e + I_h$

Generation and Recombination

The concentration of these carriers is dynamic. Due to thermal effects, electrons can jump from the valence band to the conduction band, creating an electron-hole pair; this is called generation. Conversely, when an electron falls back into a hole, the pair is annihilated; this is called recombination.

The relationship between the concentration of electrons and holes in equilibrium is governed by the Law of Mass Action, which relates them to the intrinsic carrier concentration ($n_i$):

$n_e \cdot n_h = n_i^2$

Diffusion and Potential Barriers

When there is a concentration gradient (a difference in carrier density between two regions), carriers will naturally move from the high-concentration area to the low-concentration area. This movement is called diffusion.

In a p-n junction, the diffusion of electrons from the n-side to the p-side and holes from the p-side to the n-side creates a depletion layer of ions. This layer generates an internal electric field that creates a potential barrier, which opposes further diffusion. For Silicon, this barrier (knee voltage) is approximately $0.7 \text{ V}$, while for Germanium, it is approximately $0.3 \text{ V}$.