PHYS 210Spring 2006SemiconductorsSemi-conductors probably had a larger impact on our society than any other materials discoveryin the 20th century. The wide utility of semiconductors lies in the ability to tailor their electricalproperties.1. Undoped SemiconductorsThe energy levels of an un-doped semiconductor or an insulator areshown on the right. As in any solid, electron energy levels are mergedinto continuous bands. The valence band contains as many electrons asallowed by the Fermi exclusion principle while the conduction band is empty. Electricalconductivity results from electrons moving from occupied to unoccupied energy states, so in thisstate the material in insulating. The difference between semi-conductors and insulators is that insemi-conductors the energy gap Eg between the two bands is relatively small, about 1 eV. Asmall fraction of the electrons (about exp(-kT/ Eg)) are thermally excited to the conduction bandwhere they can participate in current flow. As a result, semi-conductors have an intermediateresistively that depends exponentially on temperature. The thermistors we used in thetemperature measurement lab use that type of material.2. Doped semiconductorsSemiconductor materials, such as Si, are often doped with elements that have either one more orone less electron in the outer shell. For example, Ga has 3 valence electrons, one less than Si.When added to a Si crystal it produces “holes” – unoccupied electron states in the valence band.Similarly, As has 5 valence electrons and the extra electrons have to go into the conduction band.As a result, doped materials have much higher electrical conductivity than pure Si. The electriccurrent can be carried either by electrons (n-type semiconductor) or holes (p-type semi-conductor).3. p-n-JunctionA p-n junction is formed by bringing two doped semi-conductorstogether. Initially, electrons and holes diffuse into the other materialdue to the gradient in their concentration. However that sets up acharge imbalance that creates an electric field and eventually stopsdiffusion of the charge carriers. An applied voltage can eitherincrease or decrease this electric field. When the external voltagereduces the electric field, the p-n junction can conduct electriccurrent. Thus, the p-n junction works as a diode, i.e. conductscurrent only in one direction. p-n junctions can also convert light toelectricity and vise versa. If the electrons and holes recombine theyrelease energy equal to the band gap. This energy can be emitted asa photon. Conversely, an electron-hole pair can be created by a photon.Conduction BandValence BandEgValence BandConduction BandHolesElectronspn+−E4. Schottky DiodeA diode can also be formed on an interface of a semi-conductor and a metal. The properties ofthe interface depend on the work-function of the metal. If the top energy level of the electronsfilling the conduction band in the metal falls in between the two bands of the semiconductor thejunction acts as a diode. Schottky junctions are easy to fabricate and they can often be used inplace of p-n junctions. We will fabricate a solar cell using a Au-Si junction.5. Diode lasersAs mentioned above, electron-hole recombination can result in emission of photons. Light-emitting diodes let the photons simply escape the semi-conductor. It is also possible to constructa diode laser by recycling the photons in a cavity. The basiclayout of a laser is shown in the figure on the right. Thephotons bounce between the mirrors and stimulate additionalphoton emissions in the same direction. This is a consequenceof Bose-Einstein condensation, photons prefer to occupy thesame state. The light forms a standing wave in the cavity andsome fraction of it escapes through the mirror, forming theoutput laser beam. For laser diodes the entire cavity is about 100 µm long.Cavity MirrorsActive