Question

Silicon can be doped with small amounts of phosphorus to create a semiconductor used in transistors. (a) Is the alloy interstitial or substitutional? Justify your answer. (b) How do you expect the properties of the doped material to differ from those of pure silicon?

Short answer

The alloy is substitutional because phosphorus atoms replace silicon atoms in the lattice. Doped silicon has increased electrical conductivity compared to pure silicon.

Step-by-step solution

Understand the Types of Alloys

There are two primary types of alloys: interstitial and substitutional. Interstitial alloys occur when smaller atoms fill the spaces (or interstices) in the metallic lattice. Substitutional alloys occur when atoms replace the host metal atoms in the lattice.

Determine the Type of Alloy for Doped Silicon

Phosphorus atoms, which are similar in size to silicon atoms, replace some of the silicon atoms in the crystal lattice to create doped silicon. This is characteristic of a substitutional alloy.

Predict the Changes in Properties

By doping silicon with phosphorus, the electrical conductivity increases due to the extra valence electrons contributed by phosphorus. This process changes the semiconductor from being intrinsic to extrinsic, providing free carriers for electrical conduction.

Key concepts

Interstitial and Substitutional Alloys

Understanding the difference between interstitial and substitutional alloys is crucial when studying materials like semiconductors. Interstitial alloys are formed when smaller atoms occupy the spaces between the larger atoms in a crystal lattice. Imagine a shelf of books with small pebbles tucked in between – that’s quite analogous to an interstitial alloy. This type of alloy can occur in non-metallic materials as well.

On the other hand, substitutional alloys occur when atoms of a similar size to the host material replace some of the atoms in the lattice, similar to swapping out select books on our bookshelf with ones of similar size but different content. In the case of silicon—which forms a diamond cubic crystal structure—doping with phosphorus creates a substitutional alloy because phosphorus atoms take the place of some silicon atoms in the semiconductor's rigid crystal lattice. This substitution is made easier because silicon and phosphorus are in the same group of the periodic table, meaning they have similar atomic radii.

Semiconductor Doping

Semiconductor doping is akin to carefully adding a pinch of spice to a dish to enhance its flavor. In a semiconductor, pure silicon can be 'spiced up' by embedding a small amount of another element, such as phosphorus, to alter its electrical properties. This addition is purposeful and controlled, aiming to change the behavior of the semiconductor in a predictable way.

During this process, dopant atoms take the place of silicon atoms, thus creating a substitutional alloy. Phosphorus has one more valence electron than silicon, and when it substitutes silicon in the crystal lattice, it brings along this extra electron. This extra negatively charged electron increases the semiconductor's ability to conduct electricity by providing more charge carriers. The introduction of phosphorus changes the silicon from a 'pure' intrinsic semiconductor to an 'impure' extrinsic semiconductor with significantly improved conductivity.

Electrical Conductivity

Electrical conductivity is a measure of how well a material can allow the flow of electrical current. This characteristic is central to understanding semiconductors and how they are manipulated for use in technology. Intrinsic semiconductors, like pure silicon, have a balanced number of electrons and holes, which are positions where an electron could exist but currently does not.

Doping introduces additional charge carriers, which are mobile and can participate in electrical conduction. In the case of phosphorus doping, extra electrons become the majority charge carriers, as each phosphorus atom donates one. This excess of electrons enhances the semiconductor's electrical conductivity. The level of doping must be precise, as too much dopant can introduce defects that hinder performance, much like too much salt can ruin a meal.

Intrinsic and Extrinsic Semiconductors

Semiconductors are categorized based on their purity and electrical properties into intrinsic and extrinsic types. Intrinsic semiconductors are pure forms that have no intentional impurities added. Their electrical conductivity is limited to the charge carriers generated by the material itself, which is highly temperature dependent.

Extrinsic semiconductors, however, get their enhanced properties from doping with a specific impurity, such as phosphorus in silicon. This doping integrates additional charge carriers, transforming the balance and behavior of the semiconductor. Extrinsic semiconductors are further classified into n-type or p-type, based on the nature of the majority charge carriers (negative or positive, respectively). Phosphorus doping creates an n-type semiconductor because the dopant provides additional electrons, which are negatively charged. This tailored alteration of electrical properties is fundamental in the creation of various electronic devices, including diodes, transistors, and solar cells.