Question

The behavior of Ge as semi-conductor is due to width of: (A) Conduction band being large (B) Forbidden band being large (C) Conduction band being small (D) Forbidden band being small and narrow

Short answer

The behavior of germanium (Ge) as a semiconductor is due to the width of the forbidden band being small and narrow (option D). This allows electrons to easily transition from the valence band to the conduction band, enabling electrical conduction and the characteristic semi-conductive behavior.

Step-by-step solution

Understand the energy bands in semiconductors

In a semiconductor material like germanium, atoms are close together, and their energy levels combine to create energy bands. There are three main energy bands: 1. Valence band: The highest energy band with electrons involved in atomic bonding. 2. Conduction band: The energy band where free electrons can move through the material and participate in electrical conduction. 3. Forbidden band or bandgap: The energy gap between the valence and conduction bands where no electron states can exist.

Relate energy bands to the behavior of semiconductors

A material's conductivity heavily depends on the position of its valence and conduction bands. For a semiconductor, the forbidden band (or bandgap) is small enough that electrons can transition from the valence band to the conduction band due to thermal energy or other excitations. This allows the semiconductor to conduct electricity, and its conductivity increases with increasing temperature.

Identify the characteristic attribute of germanium

As a semiconductor, germanium has a relatively small forbidden band width, making it easier for electrons to transition to the conduction band, thereby allowing it to display its characteristic semi-conductive behavior.

Select the correct option

Based on our analysis, the behavior of germanium as a semiconductor is due to the width of the forbidden band being small and narrow. Therefore, the correct answer is: (D) Forbidden band being small and narrow

Key concepts

Conduction band

When we talk about the conduction band in semiconductors, it's where the action happens for conducting electricity. Think of the conduction band as an open highway for electrons to travel through.
In more technical terms, this is the energy band where electrons are free enough to drift throughout the material, carrying an electric current.

• In metals, this conduction band overlaps with the valence band, which is why they conduct electricity so well.
• In semiconductors, the conduction band is normally empty until electrons are excited enough to jump into it.

What energizes these electrons to hop into the conduction band? Mainly heat or light, which can supply the necessary energy to overcome the small gap between the bands.
The ease with which electrons can transition to the conduction band is integral to a semiconductor’s ability to conduct electricity.

Forbidden band

In the context of semiconductors, the forbidden band, also known as the bandgap, is crucial. This gap represents an energy range where no electron states are present.
Electrons require a certain amount of energy to leap from the valence band into the conduction band, crossing this bandgap.
The size of the forbidden band thus determines whether a material is a conductor, semiconductor, or insulator.

• Insulators have a wide forbidden band, making it difficult for electrons to bridge the gap.
• Semiconductors have a narrow bandgap, allowing electrons to easily jump across under certain conditions.
• Conductors, on the other hand, essentially have no bandgap, allowing electrons to flow freely.

In Germanium, a common semiconductor, the forbidden band is relatively small, facilitating the movement of electrons and enhancing its conductive properties, especially as temperature rises.

Valence band

The valence band is home base for electrons in a semiconductor. It's the band where electrons are tied more closely to atoms, participating in forming chemical bonds.
This band is significant because it characterizes how easily electrons can be excited into the conduction band.

• In a perfect semiconductor, the valence band is completely filled at absolute zero temperature.
• When energy is added to the system, such as by heating or applying a voltage, some electrons receive enough energy to move from the valence to the conduction band.

This movement is the pivotal step in the conduction process of a semiconductor, as it creates "holes" or vacancies in the valence band, which can also carry the current.
Thus, the behavior of electrons in the valence band is essential for understanding semiconductors' electrical properties.