band gap and conductivity

In solid-state physics, the band structure of a solid describes those ranges of energy, called energy bands, that an electron within the solid may have (“allowed bands”) and ranges of energy called band gaps (“forbidden bands”), which it may not have. Some donors have fewer valence electrons than the host, such as alkali metals, which are donors in most solids. This produces a number of molecular orbitals proportional to the number of valence electrons. Typically electrons and holes have somewhat different mobilities (µe and µh, respectively) so the conductivity is given by: For either type of charge carrier, we recall from Ch. An electron-hole pair is created by adding heat or light energy E > Egap to a semiconductor (blue arrow). A conductor is a material which contains movable electric charges. There are a number of places where we find semiconductors in the periodic table: A 2" wafer cut from a GaAs single crystal. The conductivity (σ) is the product of the number density of carriers (n or p), their charge (e), and their mobility (µ). This kind of plot, which resembles an Arrhenius plot, is shown at the right for three different undoped semiconductors. There are even conductive polymers. 4 for different widths 4, 8, 12, 16, 20 and 24. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. According to band theory, a conductor is simply a material that has its valence band and conduction band overlapping, allowing electrons to flow through the material with minimal applied voltage. Note the similarity to the equation for water autodissociation: By analogy, we will see that when we increase n (e.g., by doping), p will decrease, and vice-versa, but their product will remain constant at a given temperature. 10.5: Semiconductors- Band Gaps, Colors, Conductivity and Doping, [ "article:topic", "showtoc:no", "license:ccbysa" ], https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FInorganic_Chemistry%2FBook%253A_Introduction_to_Inorganic_Chemistry%2F10%253A_Electronic_Properties_of_Materials_-_Superconductors_and_Semiconductors%2F10.05%253A_Semiconductors-_Band_Gaps_Colors_Conductivity_and_Doping, 10.4: Periodic Trends- Metals, Semiconductors, and Insulators, information contact us at [email protected], status page at https://status.libretexts.org, Early transition metal oxides and nitrides, especially those with d, Layered transition metal chalcogenides with d. Zincblende- and wurtzite-structure compounds of the p-block elements, especially those that are isoelectronic with Si or Ge, such as GaAs and CdTe. band into the conduction band due to thermal excitation, as shown in Fig. This is why these dopants are called acceptors. Examples are anion vacancies in CdS1-x and WO3-x, both of which give n-type semiconductors, and copper vacancies in Cu1-xO, which gives a p-type semiconductor. While these are most common, there are other p-block semiconductors that are not isoelectronic and have different structures, including GaS, PbS, and Se. In this experiment, we will calculate the energy band gap in the intrinsic region and It thus appears reddish-orange (the colors of light reflected from Fe2O3) because it absorbs green, blue, and violet light. Almost all applications of semiconductors involve controlled doping, which is the substitution of impurity atoms, into the lattice. In the case of silicon, a trivalent atom is substituted into the crystal lattice. Within an energy band, energy levels can be regarded as a near continuum for two reasons: All conductors contain electrical charges, which will move when an electric potential difference (measured in volts) is applied across separate points on the material. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or … Let’s try to examine the energy diagram of the three types of materials used in electronics and discuss the conductivity of each material based on their band gap. 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. This behaviour can be better understood if one considers that the interatomic spacing increases when the amplitude of the atomic vibrations increases due to the increased thermal energy. From the tauc plot it was observed, and calculated the energy band gap increases as the particle size decreases and shown TiO 2 is direct band gap. The color of emitted light from an LED or semiconductor laser corresponds to the band gap energy and can be read off the color wheel shown at the right. If we substitute P for Si at the level of one part-per-million, the concentration of electrons is about 1016 cm-3, since there are approximately 1022 Si atoms/cm3 in the crystal. Intrinsic semiconductors are composed of only one kind of material. In conductors (metals) there is zero band gap, therefore the valence and conduction bands overlap. As noted above, the doping of semiconductors dramatically changes their conductivity. Doping atom usually have one more valence electron than one type of the host atoms. The UV–vis spectroscopy measurement modulates the bandgap with the increase in the lithium-ion concentration. The minority carriers (in this case holes) do not contribute to the conductivity, because their concentration is so much lower than that of the majority carrier (electrons). An Illustration of the Electronic Band Structure of a Semiconductor: This is a comprehensive illustration of the molecular orbitals in a bulk material. When electrons are excited across the gap, the bottom of the conduction band (CB) is populated by electrons, and the top of the valence band (VB) by holes. 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. Bands may also be viewed as the large-scale limit of molecular orbital theory. Because gold does not corrode, it is used for high-quality surface-to-surface contacts. When the dopant atom accepts an electron, this causes the loss of half of one bond from the neighboring atom, resulting in the formation of a hole. It successfully uses a material’s band structure to explain many physical properties of solids. In insulators, it is large, making it difficult for electrons to flow through the conduction band. Therefore the dopant atom can accept an electron from a neighboring atom’s covalent bond to complete the fourth bond. While insulating materials may be doped to become semiconductors, intrinsic semiconductors can also be doped, resulting in an extrinsic semiconductor. However, once each hole has wandered away into the lattice, one proton in the atom at the hole’s location will be “exposed” and no longer cancelled by an electron. Substances with large band gaps are generally insulators, those with smaller band gaps are semiconductors, while conductors either have very small band gaps or none, because the valence and conduction bands overlap. This trend can be understood by recalling that Egap is related to the energy splitting between bonding and antibonding orbitals. Copper is the most common material used for electrical wiring. As we have already discussed that the forbidden energy gap between valence and conduction band is different for different material. The band gap is a very important property of a semiconductor because it determines its color and conductivity. There are two types of extrinsic semiconductors: p-type (p for positive: a hole has been added through doping with a group -III element) and n-type (n for negative: an extra electron has been added through doping with a group-V element). Band theory models the behavior of electrons in solids by postulating the existence of energy bands. Density functional theory calculations showed that the narrowing of band gap was attributed to a finite overlap between Pb 6s and Sn 5s orbitals around the bottom of the conduction band. The p-block octet semiconductors are by far the most studied and important for technological applications, and are the ones that we will discuss in detail. The band gap is the energy needed to promote an electron from the lower energy valence band into the higher energy conduction band (Figure 1). This hole can become delocalized by promoting an electron from the valence band to fill the localized hole state. Auger electron spectrum of band gap illuminated ZnO powder sample as a function of electron energy taken at the same conditions as in fig. The energy bands correspond to a large number of discrete quantum states of the electrons. The defects facilitate the mobility of lithium ions, leading to greater Li-ion conductivity. As the energy in the system increases, electrons leave the valence band and enter the conduction band. When the doping material is added, it takes away (accepts) weakly bound outer electrons from the semiconductor atoms. For example, red and orange light-emitting diodes (LED's) are made from solid solutions with compositions of GaP0.40As0.60 and GaP0.65As0.35, respectively. Doping of semiconductors. Increasing the mole fraction of the lighter element (P) results in a larger band gap, and thus a higher energy of emitted photons. Semiconductors and insulators are distinguished from metals by the population of electrons in each band. In crystalline Si, each atom has four valence electrons and makes four bonds to its neighbors. This "law" is often violated in real materials, but nevertheless offers useful guidance for designing materials with specific band gaps. N-type Semiconductor: After the material has been doped with phosphorus, an extra electron is present. The hole, which is the absence of an electron in a bonding orbital, is also a mobile charge carrier, but with a positive charge. Doping 3. where NV and NC are the effective density of states in the valence and conduction bands, respectively. The purpose of p-type doping is to create an abundance of holes. For example, in III-V semiconductors such as gallium arsenide, silicon can be a donor when it substitutes for gallium or an acceptor when it replaces arsenic. In metallic conductors such as copper or aluminum, the movable charged particles are electrons. For this reason a hole behaves as a positive charge. For example silicon, germanium. Energy Diagrams. Semiconductors are materials that have properties of both normal conductors and insulators. The obtained data allow the determination of the n−p demarcation line in terms of temperature and oxygen activities. In silicon, this "expanded" Bohr radius is about 42 Å, i.e., 80 times larger than in the hydrogen atom. 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