Question

How are charge carriers created in an intrinsic semiconductor? Explain.

Hint:

Intrinsic = Pure. Since it's pure, there are no dopants. The only way to get charge carriers is via heat (thermal excitation), which breaks covalent bonds to create exactly one free electron and one hole simultaneously (\(n_e = n_h\)).

Answer 1

Concept: An intrinsic semiconductor is a completely pure semiconductor material (such as pure Silicon or pure Germanium) containing absolutely no deliberate chemical impurities or dopants. In these crystalline structures, every atom is covalently bonded to its four nearest neighbors using its four valence electrons. The electronic band structure of a semiconductor consists of a completely filled valence band at absolute zero temperature (\(0 \text{ K}\)) separated from an entirely empty conduction band by a narrow forbidden energy gap (\(E_g \approx 1.1 \text{ eV}\) for Silicon, \(E_g \approx 0.7 \text{ eV}\) for Germanium).

Step 1: The state of the semiconductor at Absolute Zero (\(0 \text{ K}\))
At a temperature of absolute zero, nucleons and atomic configurations possess minimal kinetic systems, and all valence electrons are locked securely within their specific local covalent bonds. Because no free electrons exist to move throughout the crystal lattice, the conduction band is devoid of charge carriers. Consequently, at \(0 \text{ K}\), an intrinsic semiconductor behaves as a perfect electrical insulator.

Step 2: Generation of charge carriers at room temperature (\(T > 0 \text{ K}\))
As the ambient temperature of the semiconductor is raised above absolute zero (such as reaching room temperature \(T \approx 300 \text{ K}\)), the atoms within the crystal lattice absorb ambient thermal energy. This causes the lattice ions to vibrate, transferring thermal kinetic energy directly to the bound valence electrons. If a valence electron absorbs a specific discrete amount of thermal energy that is equal to or greater than the forbidden energy bandgap (\(E_{\text{thermal}} \geq E_g\)), it gains enough energy to break free from its highly localized covalent bond.

Step 3: Formation of the electron-hole pair
When this thermal breaking of a bond occurs, the following simultaneous dual phenomena happen:
• Free Electron Generation: The energized electron escapes the localized valence configuration and transitions across the forbidden gap into the conduction band. Once in the conduction band, it becomes a "free electron" that can move randomly through the crystal lattice under an applied electric field, acting as a negative charge carrier.
• Hole Generation: The departure of the electron leaves behind a localized structural vacancy or deficiency of an electron within that specific covalent bond in the valence band. This vacant electronic site behaves effectively as an independent entity possessing a virtual net positive charge equal in magnitude to the electronic charge (\(+1.6 \times 10^{-19} \text{ C}\)). This positive vacancy is called a hole.

Step 4: Equilibrium condition in intrinsic semiconductors
Because every single free electron in the conduction band is created strictly by the identical physical event that leaves a corresponding vacancy in the valence band, charge carriers in intrinsic semiconductors are always generated in pairs, known as electron-hole pairs. Therefore, in any pure intrinsic semiconductor, the number density of free conduction electrons (\(n_e\)) must be exactly equal to the number density of valence holes (\(n_h\)), which is defined as the intrinsic carrier concentration (\(n_i\)): \[ n_e = n_h = n_i \] Thus, thermal excitation is the sole mechanism responsible for generating charge carriers in an intrinsic semiconductor.