Intrinsic Semiconductors

Introduction

Intrinsic semiconductors, sometimes referred to as pure semiconductors, are materials that are not doped by impurities and consist only of one type of atom. They represent an essential class of materials that have revolutionized the world of electronics and underpin the operation of devices such as transistors, diodes, and solar cells.

Basic Concept: Band Gap

Intrinsic semiconductors are characterized by their energy band structure. The band structure comprises a valence band, filled with electrons, and a conduction band, which is empty at absolute zero temperature. The energy difference between these two bands is called the band gap, denoted by .

In metals, the valence and conduction bands overlap, allowing for free movement of electrons. However, in insulators, the band gap is large, hindering electron movement. Semiconductors fall somewhere in between, with a moderate band gap that allows for controllable electron movement.

Intrinsic Carrier Concentration

One of the most important properties of intrinsic semiconductors is the intrinsic carrier concentration (), representing the number of free electrons (and holes) per unit volume when the semiconductor is in thermal equilibrium. At room temperature, a significant number of valence electrons have enough thermal energy to jump across the band gap and reach the conduction band, thereby becoming free carriers.

The intrinsic carrier concentration can be represented as:

where and are the effective densities of states in the conduction and valence bands respectively, is the energy band gap, is Boltzmann’s constant, and is the absolute temperature.

Electrical Conductivity

The electrical conductivity () of an intrinsic semiconductor can be given as:

where is the charge of an electron, is the mobility of electrons, and is the mobility of holes. Note that the number of electrons equals the number of holes in an intrinsic semiconductor, hence the factor of .

Temperature Dependence

The behavior of intrinsic semiconductors significantly depends on temperature. As temperature increases, the intrinsic carrier concentration increases exponentially due to more electrons gaining sufficient energy to cross the band gap. This results in an increase in conductivity.

Application: Photodiodes and Solar Cells

Intrinsic semiconductors play a key role in photodiodes and solar cells, where the absorption of light leads to the creation of electron-hole pairs, thereby generating current.

Conclusion

Intrinsic semiconductors provide the fundamental principles and starting point for understanding semiconductor physics. By manipulating these materials, for instance through the process of doping, we can engineer the electronic properties of semiconductors, paving the way for the fabrication of an incredibly wide range of electronic devices that have transformed modern society.

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