Introduction

What is a semiconductor?

Materials can be catagorised into conductors, semiconductors or insulators by their ability to conduct electricity. It is a popular belief that insulators do not conduct electricity because their valence electrons are not free to wander throughout the material. In fact they are free to move around, however, in an insulator there are as many electrons as there are energy levels for them to occupy. If an electron swaps place with another electron, no change is made, since individual electrons are indistinguishable. There are higher energy levels, but to promote the electrons to such a high energy levels requires an enormous voltage. Metals conduct electricity easily. In this case, the energy levels between the conduction and valence band are closely spaced and there are more levels than electrons so very little energy is required to find new energies for electrons to occupy. The resisistivity of a material is measure of how difficult it is for a current to flow. Semiconductors have a resistivity between 10^-4<r>10^{8 W} m, although these are rough limits. The band theory of materials explains qualitatively the difference between these types of materials. Electrons belong to the class of particles Fermions that have the property: only two electrons, each with opposite spin, can occupy a single energy level. As more electrons are brought together they are forced to occupy energy levels from the lowest energies upwards. However, some energy levels are forbidden because of the electrostatic potential of the crystal structure. The Kronig-Pennie model describes a simple quantum mechanical model of this.The allowed energy levels form bands. In semiconductors, the highest filled level at T=0 is known as the valence band. Electrons in the valence band do not participate in the conduction process. The first unfilled level above the valence band is known as the conduction band. The vacuum level is defined as the energy required to extract an electron from the conduction band until it is free from the potential of the crystal structure. In metals, there is no forbidden gap; the conduction band and the valence band overlap, allowing free electrons to participate in the conduction process. Insulators have an energy gap that is far greater than the thermal energy of the electron, while semiconductor materials the energy gap is typically between1-3eV. The diagram below summarises the energy band model of materials.