The band gap is a major factor determining the electrical conductivity of a solid. 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. When the doping material is added, it takes away (accepts) weakly bound outer electrons from the semiconductor atoms. Each anion (yellow) is coordinated by two cations of each type (blue and red). Visible light covers the range of approximately 390-700 nm, or 1.8-3.1 eV. The crystal is n-doped, meaning that the majority carrier (electron) is negatively charged. Some donors have fewer valence electrons than the host, such as alkali metals, which are donors in most solids. These combinations include 4-4 (Si, Ge, SiC,…), 3-5 (GaAs, AlSb, InP,…), 2-6 (CdSe, HgTe, ZnO,…), and 1-7 (AgCl, CuBr,…) semiconductors. In this experiment, we will calculate the energy band gap in the intrinsic region and It successfully uses a material’s band structure to explain many physical properties of solids. If several atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals, each with a different energy. This produces a number of molecular orbitals proportional to the number of valence electrons. However, some non-metallic materials are practical electrical conductors without being good thermal conductors. Intrinsic semiconductors are composed of only one kind of material; silicon and germanium are two examples. It is found that the conductivity increases nine times as the lithium concentration increases. In silicon, this "expanded" Bohr radius is about 42 Å, i.e., 80 times larger than in the hydrogen atom. Extrinsic semiconductors, on the other hand, are intrinsic semiconductors with other substances added to alter their properties — that is to say, they have been doped with another element. For example, the intrinsic carrier concentration in Si at 300 K is about 1010 cm-3. Sometimes it is not immediately obvious what kind of doping (n- or p-type) is induced by "messing up" a semiconductor crystal lattice. The valence band in conductors is almost vacant, in semiconductors, it is partially filled as some electrons are present in the conduction band due to small band gap. 4 for different widths 4, 8, 12, 16, 20 and 24. Depending on how they are rolled, SWNTs' band gap can vary from 0 to 2 eV and electrical conductivity can show metallic or semiconducting behavior. Sometimes, there can be both p- and n-type dopants in the same crystal, for example B and P impurities in a Si lattice, or cation and anion vacancies in a metal oxide lattice. By measuring the conductivity as a function of temperature, it is possible to obtain the activation energy for conduction, which is Egap/2. Electrical Conductivity of Semiconductor In semiconductor the valance band and conduction band are separated by a forbidden gap of sufficient width. 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 info@libretexts.org, 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. While these are most common, there are other p-block semiconductors that are not isoelectronic and have different structures, including GaS, PbS, and Se. Thus, holes are the majority carriers, while electrons become minority carriers in p-type materials. Thus semiconductors with band gaps in the infrared (e.g., Si, 1.1 eV and GaAs, 1.4 eV) appear black because they absorb all colors of visible light. Thermal and electrical conductivity often go together. When a large number of atoms (1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. This is due to the increase of grain size and removal of defects, which are present in the film. 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. The energy of these bands is between the energy of the ground state and the free electron energy (the energy required for an electron to escape entirely from the material). Y. Shapira et al./Chemisorption, photodesorption and conductivity on ZnO 55 dN dE 240 250 260 … The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. 2.2.5 Temperature dependence of the energy bandgap The energy bandgap of semiconductors tends to decrease as the temperature is increased. Doping 3. A dopant can also be present on more than one site. GaAs, like many p-block semiconductors, has the zincblende structure. Periodic Trends in Bonding Properties of Solids 2. The electron-hole pair recombines to release energy equal to Egap (red arrow). This atom will have three electrons and one hole surrounding a particular nucleus with four protons. This is why these dopants are called acceptors. In semiconductors, only a few electrons exist in the conduction band just above the valence band, and an insulator has almost no free electrons. This trend can also be understood from a simple MO picture, as we discussed in Ch. However, the valence band is completely filled in case of insulators because there exists a large band gap between valence and conduction band. Most familiar conductors are metallic. Consequently, the difference in energy between them becomes very small. There are three consequences of this calculation: Similarly, for p-type materials, the conductivity is dominated by holes, and is also much higher than that of the intrinsic semiconductor. Plots of ln(σ) vs. inverse temperature for intrinsic semiconductors Ge (Egap = 0.7 eV), Si (1.1 eV) and GaAs (1.4 eV). Positive charges may also be mobile, such as the cationic electrolyte(s) of a battery or the mobile protons of the proton conductor of a fuel cell. This release of energy is responsible for the emission of light in LEDs. The unit cell is doubled relative to the parent zincblende structure because of the ordered arrangement of cations. For solar cell applications, the semiconductor must have a wide band gap, and its electrical conductivity should be higher than that of the insulator. This trend can be understood by recalling that Egap is related to the energy splitting between bonding and antibonding orbitals. File:Isolator-metal.svg - Wikipedia, the free encyclopedia. The color of absorbed light includes the band gap energy, but also all colors of higher energy (shorter wavelength), because electrons can be excited from the valence band to a range of energies in the conduction band. Semiconductor solid solutions such as GaAs1-xPx have band gaps that are intermediate between the end member compounds, in this case GaAs and GaP (both zincblende structure). The UV–vis spectroscopy measurement modulates the bandgap with the increase in the lithium-ion concentration. The motion of holes in the lattice can be pictured as analogous to the movement of an empty seat in a crowded theater. And it is confirmed from XRD using Scherer formula and SEM, as prepared samples are studied for UV absorbance, and DC conductivity from room temperature to 400°C. We can write a mass action expression: where n and p represent the number density of electrons and holes, respectively, in units of cm-3. An Illustration of the Electronic Band Structure of a Semiconductor: This is a comprehensive illustration of the molecular orbitals in a bulk material. This difference decreases (and bonds become weaker) as the principal quantum number increases. Increasing the mole fraction of the lighter element (P) results in a larger band gap, and thus a higher energy of emitted photons. Many of the applications of semiconductors are related to band gaps: Color wheel showing the colors and wavelengths of emitted light. Other variations that add up to an octet configuration are also possible, such as CuIInIIISe2, which has the chalcopyrite structure, shown at the right. It thus appears reddish-orange (the colors of light reflected from Fe2O3) because it absorbs green, blue, and violet light. The entropy change for creating electron hole pairs is given by: \[\Delta S^{o} = R ln (N_{V}) + R ln (N_{V}) = R ln (N_{C}N_{V})\]. The energy bands correspond to a large number of discrete quantum states of the electrons. In describing conductors using the concept of band theory, it is best to focus on conductors that conduct electricity using mobile electrons. 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. Wide band gap semiconductors such as TiO2 (3.0 eV) are white because they absorb only in the UV. 2. According to the mass action equation, if n = 1016, then p = 104 cm-3. Chemistry of semiconductor doping. Semiconductors and insulators are further distinguished by the relative band gap. Fe2O3 has a band gap of 2.2 eV and thus absorbs light with λ < 560 nm. Crucial to the conductivity method is whether or not or not there ar electrons inside the conductivity band. Fe2O3 powder is reddish orange because of its 2.2 eV band gap. Many of the applications of semiconductors are related to band gaps: Narrow gap materials (Hg x Cd 1-x Te, VO 2 , InSb, Bi 2 Te 3 ) are used as infrared photodetectors and thermoelectrics (which convert heat to electricity). The purpose of p-type doping is to create an abundance of holes. The color of absorbed and emitted light both depend on the band gap of the semiconductor. This cutoff is chosen because, as we will see, the conductivity of undoped semiconductors drops off exponentially with the band gap energy and at 3.0 eV it is very low. 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. In solid-state physics, the energy gap or the band gap is an energy range between valence band and conduction band where electron states are forbidden. n- and p-type doping of semiconductors involves substitution of electron donor atoms (light orange) or acceptor atoms (blue) into the lattice. As noted above, the doping of semiconductors dramatically changes their conductivity. The promotion of an electron (e-) leaves behind a hole (h+) in the valence band. 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. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Each hole is associated with a nearby negatively charged dopant ion, and the semiconductor remains electrically neutral overall. Electrical conductivity of non-metals is determined by the susceptibility of electrons to be excited from the valence band to the conduction band. For instance, the sea of electrons causes most metals to act both as electrical and thermal conductors. Using the equations \(K_{eq} = e^{(\frac{- \Delta G^{o}}{RT})} \) and \(\Delta G^{o} = \Delta H^{o} - T \Delta S^{o}\), we can write: \[ n \times p = n_{i}^{2} = e^{(\frac{\Delta S^{o}} {R})} e^{(\frac{- \Delta H^{o}}{RT})}\]. Insulators are non-conducting materials with few mobile charges; they carry only insignificant electric currents. The conductivity (σ) is the product of the number density of carriers (n or p), their charge (e), and their mobility (µ). Missed the LibreFest? Bands and the Conductivity Properties of the Elements 2.1. Almost all applications of semiconductors involve controlled doping, which is the substitution of impurity atoms, into the lattice. In addition to substitution of impurity atoms on normal lattice sites (the examples given above for Si), it is also possible to dope with vacancies - missing atoms - and with interstitials - extra atoms on sites that are not ordinarily occupied. Such substances are known as semiconductors. Bands may also be viewed as the large-scale limit of molecular orbital theory. There are even conductive polymers. If the band gap is really big, electrons will have a hard time jumping to the conduction band, which is the reason of material’s poor conductivity. Similarly, substituting a small amount of Zn for Ga in GaAs, or a small amount of Li for Ni in NiO, results in p-type doping. In conductors (metals) there is zero band gap, therefore the valence and conduction bands overlap. 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. Doping of semiconductors. Intrinsic semiconductors are composed of only one kind of material. There are two important trends. In particular, metals have high electrical conductivity due to their lack of a band gap—with no band gap separating the valence band (normally occupied states) from the conduction band (normally unoccupied states; electrons in this band move freely through the material and are responsible for electrical conduction), a small fraction of electrons will always be in the conduction band (i.e., free). Auger electron spectrum of band gap illuminated ZnO powder sample as a function of electron energy taken at the same conditions as in fig. In metallic conductors such as copper or aluminum, the movable charged particles are electrons. A work function is the energy required to remove an electron from a metal to vacuum as a free particle. Band theory models the behavior of electrons in solids by postulating the existence of energy bands. (1) Going down a group in the periodic table, the gap decreases: Egap (eV): 5.4 1.1 0.7 0.0. The opposite process of excitation, which creates an electron-hole pair, is their recombination. The name “extrinsic semiconductor” can be a bit misleading. • The intrinsic conductivity and intrinsic carrier concentrations are largely controlled by E g / k BT, the ratio of the band gap … 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). 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. Pure (undoped) semiconductors can conduct electricity when electrons are promoted, either by heat or light, from the valence band to the conduction band. Therefore the dopant atom can accept an electron from a neighboring atom’s covalent bond to complete the fourth bond. In semiconductor production, doping intentionally introduces impurities into an extremely pure, or intrinsic, semiconductor for the purpose of changing its electrical properties. In both cases, the effective band gap is substantially decreased, and the electrical conductivity at a given temperature increases dramatically. In crystalline Si, each atom has four valence electrons and makes four bonds to its neighbors. 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. P-type Semiconductor: After the material has been doped with boron, an electron is missing from the structure, leaving a hole. Some simple rules are as follows: For example, when TiO2 is doped with Nb on some of the Ti sites, or with F on O sites, the result is n-type doping. This creates an excess of negative (n-type) electron charge carriers. These are also called “undoped semiconductors” or “i-type semiconductors. Nonmetals: Strong Covalent Bonding 1.3. An electron-hole pair is created by adding heat or light energy E > Egap to a semiconductor (blue arrow). 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. The band gap determined from the electronic component of the electrical conductivity is 3.1 eV. Bonding in Elemental Solids 1.1. band into the conduction band due to thermal excitation, as shown in Fig. As a result, the separation between energy levels is of no consequence. Table 1. The intrinsic carrier concentration, ni, is equal to the number density of electrons or holes in an undoped semiconductor, where n = p = ni. As the energy in the system increases, electrons leave the valence band and enter the conduction band. The impurities would cause a change in conductivity, as conductivity is based on the number of holes or electrons in the valence or conduction bands of the semiconductor. Semiconductors, as we noted above, are somewhat arbitrarily defined as insulators with band gap energy < 3.0 eV (~290 kJ/mol). File:P-doped Si.svg - Wikibooks, open books for an open world. These substitutions introduce extra electrons or holes, respectively, which are easily ionized by thermal energy to become free carriers. 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. n- and p-type doping. If you are talking about photoconductivity, then smaller energy band gap means better conductivity. Metals: Weak Covalent Bonding 1.2. A conductor is a material which contains movable electric charges. Temperature dependence of the carrier concentration. 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. A conductor is a material that is able to conduct electricity with minimal impedance to the electrical flow. For pure Si (Egap = 1.1 eV) with N ≈ 1022/cm3, we can calculate from this equation a carrier density ni of approximately 1010/cm3 at 300 K. 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. While insulating materials may be doped to become semiconductors, intrinsic semiconductors can also be doped, resulting in an extrinsic semiconductor. This allows for easier electron flow. 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. Zincblende- and wurtzite-structure semiconductors have 8 valence electrons per 2 atoms. • The band gap is the difference between the lowest point of the conduction band (the conduction band edge) and the highest point in the valence band (the valence band edge). The result is that one electron is missing from one of the four covalent bonds normally part of the silicon lattice. Thus, in solids the levels form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. Conductors, Semiconductors and Insulators: On the left, a conductor (described as a metal here) has its empty bands and filled bands overlapping, allowing excited electrons to flow through the empty band with little push (voltage). N-type semiconductors are a type of extrinsic semiconductor in which the dopant atoms are capable of providing extra conduction electrons to the host material (e.g. 3. When a sufficiently large number of acceptor atoms are added, the holes greatly outnumber thermally excited electrons. CC licensed content, Specific attribution, http://en.wikipedia.org/wiki/Electrical_conductor, http://en.wikipedia.org/wiki/Electronic_band_structure, http://en.wiktionary.org/wiki/molecular_orbital, http://en.wikipedia.org/w/index.php?title=File:Isolator-metal.svg&page=1, http://en.wikipedia.org/wiki/P-type_semiconductor, http://en.wikipedia.org/wiki/Doping_(semiconductor), http://en.wikipedia.org/wiki/Semiconductor, http://en.wikipedia.org/wiki/N-type_semiconductor, http://en.wikibooks.org/wiki/Semiconductors/What_is_a_Semiconductor, http://en.wiktionary.org/wiki/semiconductor, http://en.wikibooks.org/w/index.php?title=File:P-doped_Si.svg&page=1, http://en.wikibooks.org/w/index.php?title=File:N-doped_Si.svg&page=1, http://en.wikibooks.org/wiki/Semiconductors/What_is_a_Semiconductor%23Extrinsic_Semiconductors. How does the band gap energy vary with composition? 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