Equation relating band gap energy and wavelength relationship

Band gap - Wikipedia

equation relating band gap energy and wavelength relationship

The energy of the band gap matches the energy of the photon as an electron use the equation representing the energy of a photon and solve for wavelength. How can we calculate the conductivity from energy band gap? is no direct relation between conductivity and band gap as Fermi level is not at the middle of the. As h and c are both constants, photon energy changes in inverse relation to wavelength λ. To find the photon energy in electronvolts.

Electrons and holes in semiconductors Pure undoped semiconductors can conduct electricity when electrons are promoted, either by heat or light, from the valence band to the conduction band.

equation relating band gap energy and wavelength relationship

The hole, which is the absence of an electron in a bonding orbital, is also a mobile charge carrier, but with a positive charge. The motion of holes in the lattice can be pictured as analogous to the movement of an empty seat in a crowded theater.

equation relating band gap energy and wavelength relationship

An empty seat in the middle of a row can move to the end of the row to accommodate a person arriving late to the movie if everyone moves over by one seat. Because the movement of the hole is in the opposite direction of electron movement, it acts as a positive charge carrier in an electric field.

The opposite process of excitation, which creates an electron-hole pair, is their recombination. When a conduction band electron drops down to recombine with a valence band hole, both are annihilated and energy is released. This release of energy is responsible for the emission of light in LEDs.

At equilibrium, the creation and annihilation of electron-hole pairs proceed at equal rates. We can write a mass action expression: Note the similarity to the equation for water autodissociation: This is about 12 orders of magnitude lower than the valence electron density of Al, the element just to the left of Si in the periodic table.

Thus we expect the conductivity of pure semiconductors to be many orders of magnitude lower than those of metals.

Photon energy

This kind of plot, which resembles an Arrhenius plot, is shown at the right for three different undoped semiconductors. Very small amounts of dopants in the parts-per-million range dramatically affect the conductivity of semiconductors. For this reason, very pure semiconductor materials that are carefully doped - both in terms of the concentration and spatial distribution of impurity atoms - are needed. This is exactly the right number of electrons to completely fill the valence band of the semiconductor.

equation relating band gap energy and wavelength relationship

Introducing a phosphorus atom into the lattice the yellow atom in the figure at the right adds an extra electron, because P has five valence electrons and only needs four to make bonds to its neighbors. The extra electron, at low temperature, is bound to the phosphorus atom in a hydrogen-like molecular orbital that is much larger than the 3s orbital of an isolated P atom because of the high dielectric constant of the semiconductor.

The energy needed to ionize this electron - to allow it to move freely in the lattice - is only about meV, which is not much larger the thermal energy 26 meV at room temperature.

  • Energy of Photon
  • 10.4 Semiconductors: band gaps, colors, conductivity and doping

Therefore the Fermi level lies just below the conduction band edge, and a large fraction of these extra electrons are promoted to the conduction band at room temperature, leaving behind fixed positive charges on the P atom sites. Boron has only three valence electrons, and "borrows" one from the Si lattice, creating a positively charged hole that exists in a large hydrogen-like orbital around the B atom. This hole can become delocalized by promoting an electron from the valence band to fill the localized hole state.

Again, this process requires only meV, and so at room temperature a large fraction of the holes introduced by boron doping exist in delocalized valence band states. These substitutions introduce extra electrons or holes, respectively, which are easily ionized by thermal energy to become free carriers.

Energy of Photon | PVEducation

The Fermi level of a doped semiconductor is a few tens of mV below the conduction band n-type or above the valence band p-type. Every solid has its own characteristic energy-band structure.

Electromagnetic Spectrum Explained - Gamma X rays Microwaves Infrared Radio Waves UV Visble Light

This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials. In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden from other regions. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to jump from one band to another. However, in order for an electron to jump from a valence band to a conduction band, it requires a specific minimum amount of energy for the transition.

The required energy differs with different materials. Electrons can gain enough energy to jump to the conduction band by absorbing either a phonon heat or a photon light. A semiconductor is a material with an intermediate sized but non-zero band gap that behaves as an insulator at absolute zero but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point.

In contrast, a material with a large band gap is an insulator. In conductorsthe valence and conduction bands may overlap, so they may not have a band gap.

equation relating band gap energy and wavelength relationship