Question

Explain why the electrical conductivity of a semiconductor is significantly increased if trace amounts of either donor or acceptor atoms are present, but is unchanged if both are present in equal number.

Short answer

Trace amounts of either donor or acceptor atoms in a semiconductor can significantly increase its conductivity as these can respectively donate electrons to the conduction band or accept electrons from the valence band, effectively increasing the number of charge carriers. However, if both donor and acceptor atoms are equally present, they neutralize each other's effects, thus leaving the conductivity unchanged.

Step-by-step solution

Understanding Semiconductors and Conductivity

In a pure semiconductor, the number of free charge carriers (electrons and holes) is determined by the intrinsic properties of the material, including the temperature. Electrons can move from the valence band to the conduction band, and this movement increases the electrical conductivity of the semiconductor.

Role of Donor and Acceptor Atoms

Impurities can alter the number of free charge carriers. A donor atom, with one more valence electron, can supply an extra electron to the conduction band when sufficiently energized. This increases the amount of free charge carriers and thus the conductivity. Acceptor atoms, with one less valence electron, are able to accept an electron from the valence band, leaving a hole. This hole behaves as a positive charge carrier and also increases the conductivity.

Equal Numbers of Donor and Acceptor Atoms

If there are an equal amounts of donor and acceptor atoms, an electron donated by a donor atom can be accepted by an acceptor atom. This transfer neutralises the effect of each type of dopant atom and the number of free charge carriers (and therefore the conductivity) remains the same as in the intrinsic semiconductor.

Key concepts

Electrical Conductivity

Electrical conductivity is a measure of how easily electric current can flow through a material. In semiconductors, this property is particularly interesting because it can be modified under various conditions. Unlike metals, where conductivity remains generally constant due to free electrons, semiconductors have conductivity that depends on their temperature and the presence of impurities.

In semiconductors, the electrons and holes (lack of electrons) play a crucial role. When an electron moves from the valence band up to the conduction band, it leaves behind a hole. This movement creates enough energy for the electric current to flow. With pure semiconductors, this process happens naturally and the material's intrinsic properties, such as how its atoms are structured, greatly influence its conductivity.

External factors, like increased temperature, can excite more electrons to jump to the conduction band. This leads to increased conductivity as more charge carriers are available. Without any added impurities, these changes are solely based on the intrinsic nature of the material.

Donor Atoms

Donor atoms are impurities added to a semiconductor to increase its electrical conductivity. These atoms typically have one more valence electron than the semiconductor itself. For example, if you add a phosphorus atom to silicon—considering silicon has four valence electrons—phosphorus provides an extra fifth electron.

This additional electron enters the conduction band, contributing to the pool of charge carriers. More charge carriers mean better conductivity. Thus, by carefully introducing small amounts of donor atoms into a semiconductor, its conductivity can be finely tuned.

• Donor atoms donate electrons.
• They increase the number of free electrons in the conduction band.
• This results in an increase in the material's electrical conductivity.

Acceptor Atoms

Acceptor atoms are elements with one less valence electron than the semiconductor. For instance, boron is an acceptor when mixed with silicon. Boron has three valence electrons compared to silicon's four. As an acceptor atom enters the semiconductor, it creates a spot (or a hole) that can "accept" an electron.

These holes function as positive charge carriers, moving through the semiconductor as an electron fills one hole and leaves behind another. This movement of holes also contributes to the passage of electric current just like electrons in the conduction band. By introducing acceptor atoms, semiconductors gain extra holes, augmenting their overall conductivity.

• Acceptor atoms create holes by accepting electrons.
• These holes act as positive charge carriers.
• The presence of holes enhances the material's conductivity.

Charge Carriers

Charge carriers are the essential players in the dance of electrical conductivity within semiconductors. There are two main types: electrons and holes. Electrons are negatively charged, and when they move, they create an electric current. Holes, while not actual particles, represent the absence of electrons and move through the semiconductor by allowing electrons to shuffle from one position to the next.

The interplay between electrons and holes defines a semiconductor's behavior. When a semiconductor is doped with either donor or acceptor atoms, it changes the balance of these charge carriers, increasing electrical conductivity. However, if both donor and acceptor atoms are added in equal measure, they essentially cancel each other out. Donor atoms provide extra electrons while acceptor atoms create holes. When matched, these changes neutralize, retaining the intrinsic number of charge carriers and thus maintaining original conductivity levels.

Understanding charge carriers is vital for manipulating and optimizing semiconductor devices, as their presence directly influences efficiency.