Question

Explain how doping silicon with either phosphorus or gallium increases the electrical conductivity over that of pure silicon.

Short answer

Doping silicon with phosphorus (n-type) introduces additional free electrons into the crystal lattice, increasing the number of charge carriers and thus electrical conductivity. Conversely, doping with gallium (p-type) creates "holes" due to the shortage of electrons for covalent bonding, allowing electron movement and effectively increasing positive charge carriers, which also contributes to higher electrical conductivity. The increased charge carriers in both n-type and p-type doping lead to increased electrical conductivity in doped silicon compared to pure silicon.

Step-by-step solution

Understanding Semiconductors

Semiconductors like silicon are materials with an electrical conductivity that falls between that of a conductor (like metals) and an insulator (like rubber). The electrical properties of a semiconductor are determined by its band structure, i.e., the arrangement of energy levels governing the behavior of electrons in the material. In semiconductors, there's a gap called the bandgap between the valence band (fully occupied by electrons) and the conduction band (partially or completely unoccupied by electrons). When an electron jumps from the valence band to the conduction band, it leaves behind a "hole" which can be occupied by other electrons, resulting in electrical charge movement and thus conductivity.

The concept of Doping

Silicon in its pure form is not very conductive. To increase its conductivity, a process called "doping" is used: introducing a small amount of another element (called a dopant) into the silicon crystal lattice. The dopants introduce additional energy levels within the bandgap that make it easier for electrons to move from the valence band to the conduction band. There are two types of doping: n-type (negative) and p-type (positive). For n-type doping, a dopant is used that has more valence electrons than silicon, like phosphorus, while for p-type doping, a dopant with fewer valence electrons like gallium is used.

N-Type Doping with Phosphorus

When silicon is doped with phosphorus, an element with 5 valence electrons, the extra electron that phosphorus brings to the crystal lattice cannot form a covalent bond with the surrounding silicon atoms (which have 4 valence electrons). This extra electron is relatively free to move within the lattice and contribute to electrical conductivity. As a result, n-type doped silicon has an increased number of free electrons that can participate in the conduction process, leading to higher electrical conductivity.

P-Type Doping with Gallium

On the other hand, when silicon is doped with gallium, an element with 3 valence electrons, there is a shortage of electrons to form covalent bonds with the surrounding silicon atoms. This leaves a "hole" in the crystal lattice that neighboring electrons can move into. The movement of these electrons creates an effectively positive charge carrier (the hole), which can participate in the conduction process, leading to higher electrical conductivity. In conclusion, doping silicon with phosphorus or gallium increases the number of charge carriers (free electrons for n-type doping and holes for p-type doping) in the material, which in turn increases electrical conductivity over that of pure silicon.