# Semiconductors band gap of germanium and

To measure the leakage current in a germanium diode and use this data to calculate the energy "gap" Background: This is only explainable through a quantum mechanical analysis of a solid. By approximating the crystal as being infinitely large, and using Bloch's theorem, one can deduce that there are energy gaps in allowed states in the solid. Fermi Level "Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics. Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy states.

So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface.

The concept of the Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids. Both ordinary electrical and thermal processes involve energies of a small fraction of an electron volt.

But the Fermi energies of metals are on the order of electron volts. This implies that the vast majority of the electrons cannot receive energy from those processes because there are no available energy states for them to go to within a fraction of an electron volt of their present energy.

Limited to a tiny depth of energy, these interactions are limited to " ripples on the Fermi sea ". At higher temperatures a certain fraction, characterized by the Fermi functionwill exist above the Fermi level. The Fermi level plays an important role in the band theory of solids. In doped semiconductors, p-type and n-typethe Fermi level is shifted by the impurities, illustrated by their band gaps. The Fermi level is referred to as the electron chemical potential in other contexts.

In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction.

The amount of energy which can be given to an electron in such conduction processes is on the order of micro-electron volts see copper wire exampleso only those electrons very close to the Fermi energy can participate.

The Fermi velocity of these conduction electrons can be calculated from the Fermi energy. For a metal, the density of conduction electrons can be implied from the Fermi energy.

The Fermi energy also plays an important role in understanding the mystery of why electrons do not contribute significantly to the specific heat of solids at ordinary temperatures, while they are dominant contributors to thermal conductivity and electrical conductivity.

Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat capacity by the Pauli principle.

At very low temperatures, the electron specific heat becomes significant.BAND Behavior of electrons near the bandedges determines most device properties. Near the bandedges the electrons can be described by simple effective mass pictures, i.e., the electrons behave as if they are in free space except their masses are m*.

Schematic of the valence band, direct bandgap, and indirect bandgap conduction bands. Electricity - Conductors, insulators, and semiconductors: Materials are classified as conductors, insulators, or semiconductors according to their electric conductivity.

The classifications can be understood in atomic terms. Electrons in an atom can have only certain well-defined energies, and, depending on their energies, the electrons are said to occupy particular energy levels.

Semiconductor: Semiconductor, any of a class of crystalline solids intermediate in electrical conductivity between a conductor and an insulator.

Semiconductors are employed in the manufacture of various kinds of electronic devices, including diodes, transistors, and integrated circuits.

## DoITPoMS - TLP Library Introduction to Semiconductors - Direct and Indirect Band Gap Semiconductors

= This could be acquired by engineering the compound's band gap by monitoring the amount of germanium put into the mix It needs to be thoroughly monitored, to obtain the desired band gap and avoid lattice defects and unstable films.

amorphous germanium film is a semiconductor (Nc = 4, i.e., same as in the crystalline state) while liquid germanium is a metal (Nc = 5 or higher). Various theoretical attempts have been made to study the band structure of disordered systems.4 What are the changes (e.g., in band gap).

Thus in n-doped semiconductors the donator energy level is close to the conduction band edge, the band gap to overcome is very small. Analog, through introduction of a 3-valent dopant in a semiconductor, a hole is available, which may be already occupied at low-energy by an electron from the valence band of the silicon.

Band gap - Wikipedia