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Electroreflectance (also: electromodulated reflectance) is the change of reflectivity of a solid due to the influence of an electric field close to, or at the interface of the solid with a liquid. The change in reflectivity is most noticeable at very specific ranges of photon energy, corresponding to the band gaps at critical points of the Brillouin zone. The electroreflectance effect can be used to get a clearer picture of the band structure at critical points where there is a lot of near degeneracy. Normally, the band structure at critical points (points of special interest) has to be measured within a background of adsorption from non-critical points at the Brillouin zone boundary. Using a strong electric field, the adsorption spectrum can be changed to a spectrum that shows peaks at these critical points, essentially lifting the critical points from the background. The effect was first discovered and understood in semiconductor materials, but later research proved that metals also exhibit electroreflectance. An early observation of the changing optical reflectivity of gold due to a present electric field was attributed to a change in refractive index of the neighboring liquid. However, it was shown that this could not be the case. The new conclusion was that the effect had to come from a modulation of the near-surface layer of the gold. Theoretic description Effect of the electric field on the electronic structure When an electric field is applied to a metal or semiconductor, the electronic structure of the material changes. The electrons (and other charged particles) will react to the electric field, by repositioning themselves within the material. Electrons in metals can relatively easily move around and are available in abundance. They will move in such a manner that they try to cancel the external electric field. Since no metal is a perfect conductor, no metal will perfectly cancel the external electric field within the material. In semiconductors the electrons that are available will not be able to move around as easily as electrons in metals. This leads to a weaker response and weaker cancellation of the electric field. This has the effect that the electric field can penetrate deeper into a semiconductor than into a metal. The optical reflectivity of a (semi-)conductor is based on the band structure of the material close to or at the surface of the material. For reflectivity to occur a photon has to have enough energy to overcome the bandgap of electrons at the Fermi surface. When the photon energy is smaller than the bandgap, the solid will be unable to absorb the energy of the photon by excitation of an electron to a higher energy. This means that the photon will not be re-emitted by the solid and thus not reflected. If the photon energy is large enough to excite an electron from the Fermi surface, the solid will re-emit the photon by decaying the electron back to the original energy. This is not exactly the same photon as the incident photon, as it has for example the opposite direction of the incident photon. By applying an electric field to the material, the band structure of the solid changes. This change in band structure leads to a different bandgap, which in turn leads to a difference in optical reflectivity. The electric field, generally made by creating a potential difference, leads to an altered Hamiltonian. Using analytical methods available, such as the Tight Binding method, it can be calculated that this altered Hamiltonian leads to a different band structure. The combination of electron repositioning and the change in band structure due to an external electric field is called the field effect. Since the electric field has more influence on semiconductors than on metals, semiconductors are easier to use to observe the electroreflectance effect. Near the surface The optical reflection in (semi-)conductors happens mostly in the surface region of the material. Therefore, the band structure of this region is extra important. Band structure usually covers bulk material. For deviations from this structure, it is conventional to use a band diagram. In a band diagram the x-axis is changed from wavevector k in band structure diagrams to position x in the preferred direction. Usually, this positional direction is normal to the surface plane. For semiconductors specifically, the band diagram near the surface of the material is important. When an electric field is present close to, or in the material, this will lead to a potential difference within the semiconductor. Dependent on the electric field, the semiconductor will become n- or p-like in the surface region. From now on we will use that the semiconductor has become n-like at the surface. The bands near the surface will bend under the electrostatic potential of the applied electric field. This bending can be interpreted in the same way as the bending of the valence and conduction bands in a p-n-junction, when equilibrium has been reached. The result of this bending leads to a conduction band that comes close to the Fermi level. Therefore, the conduction band will begin to fill with electrons. This change in band structure leads to a change in optical reflection of the semiconductor. Brillouin zones and optical reflectivity Optical reflectivity and the Brillouin zones are closely linked, since the band gap energy in the Brillouin zone determines if a photon is absorbed or reflected. If the band gap energy in the Brillouin zone is smaller than the photon energy, the photon will be absorbed, while the photon will be transmitted/reflected if the band gap energy is larger than the photon energy. For example, the photon energies of visible light lie in a range between 1.8 eV (red light) and 3.1 eV (violet light), So if the band gap energy is larger than 3.2 eV, photons of visible light will not be absorbed, but reflected/transmitted: the material appears transparent. This is the case for diamond, quartz etc. But if the band gap is roughly 2.6 eV (this is the case for cadmium sulfide) only blue and violet light is absorbed, while red and green light are transmitted, resulting in a reddish looking material. When an electric field is added to a (semi)conductor, the material will try to cancel this field by inducing an electric field at its surface. Because of this electric field, the optical properties of the surface layer will change, due to the change in size of critical band gaps, and hence changing its energy. Since the change in band gap only occurs on the surface of the (semi)conductor, optical properties will not change in the core of bulk materials, but for very thin films, where almost all particles can be found at the surface, the optical properties can change: absorption or transmittance of certain wavelengths depending on the strength of the electric field. This can result in more accurate measurements in case there are multiple compounds in the semiconductor, practically canceling the backgr.... Discover the Christian Krammer popular books. Find the top 100 most popular Christian Krammer books.