Question

The number of holes and electrons in an intrinsic conductors are $\mathrm{x}$ and $\mathrm{y}$ respectively at room temperature. Which of the following options are true? (A) $x>y$ (B) $\mathrm{y}>\mathrm{x}$ (C) $x=y$ (D) \(x<

Short answer

In an intrinsic conductor at room temperature, the number of holes (x) and electrons (y) are equal due to the equilibrium conditions. Thus, the correct relationship is $x=y$, making option (C) the true statement.

Step-by-step solution

Understand intrinsic conductors

Intrinsic conductors are pure semiconductor materials with no impurities. At room temperature, they have a nearly equal balance of electrons and holes, the charge carriers responsible for electrical conductivity.

Equilibrium conditions

At room temperature, an intrinsic conductor is in equilibrium, which means that the rate of generation and recombination of charge carriers are equal. This balance results in equal concentrations of electrons and holes in the material.

Determine the relationship between x and y

Since intrinsic conductors have equal concentrations of electrons and holes in equilibrium at room temperature, we can state that the number of electrons (y) is equal to the number of holes (x). Therefore, the correct relationship is: $x=y$. Now we can identify which of the given options is true.

Select the correct option

After determining that the relationship between x and y is $x=y$, we can identify option (C) as the correct answer: (C) x=y

Key concepts

Charge Carriers

Charge carriers are essential components in semiconductors because they enable electrical conduction. In intrinsic semiconductors, two main types of charge carriers exist: electrons and holes.
Electrons are negatively charged particles that can move freely through the crystal lattice of the semiconductor material. Holes, on the other hand, are not real particles but rather a conceptual representation of the absence of an electron within the lattice. When an electron leaves its position, it creates a hole, which behaves as a positively charged particle.
In electrical terms, the movement of electrons and holes can be compared to the flow of positive and negative charges in a circuit. Electrons move from high to low energy states, while holes move in the opposite direction, filling in the spaces left by transmitted electrons. This dual movement of charge carriers enables intrinsic semiconductors to conduct electricity effectively.

Equilibrium Conditions

Equilibrium conditions in a semiconductor refer to a state where the rates of generation and recombination of charge carriers are equal. This balance is crucial in maintaining the stability of semiconductors.
In an intrinsic semiconductor at room temperature, equilibrium ensures that there are equal numbers of electrons and holes. This equal generation is the result of thermal energy providing just enough energy to break some of the covalent bonds in the crystalline structure, freeing electrons and creating an equal number of holes.
It's important to note that external factors like exposure to light or applied voltage can disturb this equilibrium. When this equilibrium is disturbed, the numbers of electrons and holes can vary, affecting the semiconductor's conductive properties.

Electron-Hole Pair

An electron-hole pair is a fundamental concept in semiconductor physics, referring to the simultaneous creation of a free electron and a hole.
When sufficient energy, usually provided in the form of heat or light, is applied to an intrinsic semiconductor, it can free electrons from their covalent bonds. This act of freeing an electron results in the formation of a hole at the site of the missing electron.
Together, the free electron and its corresponding hole form what is known as an electron-hole pair. These pairs are intrinsically linked because they result from the same energy event. The continuous generation and recombination of electron-hole pairs sustain the semiconductor's ability to conduct electricity at equilibrium.

Semiconductor Materials

Semiconductor materials have unique characteristics that distinguish them from conductors and insulators. The most common semiconductor materials include silicon, germanium, and gallium arsenide.
These materials are characterized by their band-gap energy, which is the energy needed to move electrons from the valence band to the conduction band. The band-gap energy in semiconductors is intermediate compared to conductors, which have near zero band-gaps, and insulators which have large band-gaps.
Intrinsic semiconductor materials are pure and do not contain any impurities. This purity ensures that the properties of the material are governed solely by the intrinsic properties of its crystal lattice. At room temperature, thermal energy is enough to partially overcome the band-gap energy, allowing for the formation of electron-hole pairs and thus enabling electrical conduction.