# band gap and conductivity

Doping 3. 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. 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). Increasing the mole fraction of the lighter element (P) results in a larger band gap, and thus a higher energy of emitted photons. A p-type (p for “positive”) semiconductor is created by adding a certain type of atom to the semiconductor in order to increase the number of free charge carriers. While these are most common, there are other p-block semiconductors that are not isoelectronic and have different structures, including GaS, PbS, and Se. It's basically a barrier energy between the "electron gas" of the metal and an external vacuum. 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. Conductivity Properties of the Elements 2.2. As the energy in the system increases, electrons leave the valence band and enter the conduction band. 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. In both cases, the impurity atom has one more valence electron than the atom for which it was substituted. N-type Semiconductor: After the material has been doped with phosphorus, an extra electron is present. 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. The band gap determined from the electronic component of the electrical conductivity is 3.1 eV. 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). At equilibrium, the creation and annihilation of electron-hole pairs proceed at equal rates. This trend can also be understood from a simple MO picture, as we discussed in Ch. Intrinsic semiconductors are composed of only one kind of material; silicon and germanium are two examples. Apply the concept of band theory to explain the behavior of conductors. 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. For phase (III), the temperature dependence of conductivity can be modelled as an exponential function where is the band gap energy, is the Boltzmann constant and is the absolute temperature. The electrical conductivity data are considered in terms of the components related to electrons, holes, and ions. File:P-doped Si.svg - Wikibooks, open books for an open world. The dependence of SWNTs electrical conductivity on the (n, m) values is shown in Table 1. There are two important trends. It is observed that the conductivity increases with the increase of temperature. 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. 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). Semiconductors, as we noted above, are somewhat arbitrarily defined as insulators with band gap energy < 3.0 eV (~290 kJ/mol). Wide band gap semiconductors such as TiO2 (3.0 eV) are white because they absorb only in the UV. By measuring the conductivity as a function of temperature, it is possible to obtain the activation energy for conduction, which is Egap/2. 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. An Illustration of the Electronic Band Structure of a Semiconductor: This is a comprehensive illustration of the molecular orbitals in a bulk material. In crystalline Si, each atom has four valence electrons and makes four bonds to its neighbors. Fe2O3 has a band gap of 2.2 eV and thus absorbs light with λ < 560 nm. 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. Bands may also be viewed as the large-scale limit of molecular orbital theory. 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. The motion of holes in the lattice can be pictured as analogous to the movement of an empty seat in a crowded theater. 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. Alternatively, boron can be substituted for silicon in the lattice, resulting in p-type doping, in which the majority carrier (hole) is positively charged. Band theory, where the molecular orbitals of a solid become a series of continuous energy levels, can be used to explain the behavior of conductors, semiconductors and insulators. These substitutions introduce extra electrons or holes, respectively, which are easily ionized by thermal energy to become free carriers. Extrinsic semiconductors are made of intrinsic semiconductors that have had other substances added to them to alter their properties (they have been doped with another element ). This is due to the increase of grain size and removal of defects, which are present in the film. Band theory models the behavior of electrons in solids by postulating the existence of energy bands. In both cases, the effective band gap is substantially decreased, and the electrical conductivity at a given temperature increases dramatically. For example, the intrinsic carrier concentration in Si at 300 K is about 1010 cm-3. An electron-hole pair is created by adding heat or light energy E > Egap to a semiconductor (blue arrow). 2.2.5 Temperature dependence of the energy bandgap The energy bandgap of semiconductors tends to decrease as the temperature is increased. 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 … 3. Semiconductors and insulators are distinguished from metals by the population of electrons in each band. 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. The purpose of p-type doping is to create an abundance of holes. Periodic Trends in Bonding Properties of Solids 2. It thus appears reddish-orange (the colors of light reflected from Fe2O3) because it absorbs green, blue, and violet light. 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. A conductor is a material which contains movable electric charges. Semiconductors are materials that have properties of both normal conductors and insulators. Legal. The electron-hole pair recombines to release energy equal to Egap (red arrow). 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. 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: $n \times p = n_{i}^{2} = e^{(\frac{\Delta S^{o}} {R})} e^{(\frac{- \Delta H^{o}}{RT})}$. When a semiconductor is doped to such a high level that it acts more like a conductor than a semiconductor, it is referred to as degenerate. Most of the states with low energy (closer to the nucleus ) are occupied, up to a particular band called the valence band. where NV and NC are the effective density of states in the valence and conduction bands, respectively. This is why these dopants are called acceptors. The UV–vis spectroscopy measurement modulates the bandgap with the increase in the lithium-ion concentration. Nonmetals: Strong Covalent Bonding 1.3. Similarly, CdS (Egap = 2.6 eV) is yellow because it absorbs blue and violet light. Very small amounts of dopants (in the parts-per-million range) dramatically affect the conductivity of semiconductors. This produces a number of molecular orbitals proportional to the number of valence electrons. The opposite process of excitation, which creates an electron-hole pair, is their recombination. 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. In most materials, the direct current is proportional to the voltage (as determined by Ohm’s law), provided the temperature remains constant and the material remains in the same shape and state. 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 obtained data allow the determination of the n−p demarcation line in terms of temperature and oxygen activities. Watch the recordings here on Youtube! In semiconductors, only a few electrons exist in the conduction band just above the valence band, and an insulator has almost no free electrons. Semiconductors and insulators have a greater and greater energetic difference between the valence band and the conduction bands, requiring a larger applied voltage in order for electrons to flow. Taking an average of the electron and hole mobilities, and using n = p, we obtain, $\mathbf{\sigma= \sigma_{o} e^{(\frac{-E_{gap}}{2kT})}}, \: where \: \sigma_{o} = 2(N_{C}N_{V})^{\frac{1}{2}}e\mu$. 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. 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. Missed the LibreFest? This separation is comparable with the energy uncertainty due to the Heisenberg uncertainty principle for reasonably long intervals of time. In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. The Fermi level (the electron energy level that has a 50% probability of occupancy at zero temperature) lies just above the valence band edge in a p-type semiconductor. When the gap between the valence band and conduction band is small, some electrons may jump from valence band to conduction band and thus show some conductivity. For instance, the sea of electrons causes most metals to act both as electrical and thermal conductors. Plots of ln(σ) vs. inverse temperature for intrinsic semiconductors Ge (Egap = 0.7 eV), Si (1.1 eV) and GaAs (1.4 eV). This release of energy is responsible for the emission of light in LEDs. This allows for easier electron flow. n- and p-type doping. The unit cell is doubled relative to the parent zincblende structure because of the ordered arrangement of cations. Visible light covers the range of approximately 390-700 nm, or 1.8-3.1 eV. If several atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals, each with a different energy. In semiconductors, the band gap is small, allowing electrons to populate the conduction band. In conductors (metals) there is zero band gap, therefore the valence and conduction bands overlap. When the doping material is added, it takes away (accepts) weakly bound outer electrons from the semiconductor atoms. 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. band into the conduction band due to thermal excitation, as shown in Fig. The name “extrinsic semiconductor” can be a bit misleading. n- and p-type doping of semiconductors involves substitution of electron donor atoms (light orange) or acceptor atoms (blue) into the lattice. For this reason a hole behaves as a positive charge. A band gap is an energy range in a solid where no electron states can exist due to the quantization of energy. Introducing a phosphorus atom into the lattice (the positively charged 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. As the energy in the system increases, electrons leave the valence band and enter the conduction band. Electrical Conductivity of Semiconductor In semiconductor the valance band and conduction band are separated by a forbidden gap of sufficient width. The slope of the line is -Egap/2k. Semiconductors and insulators are further distinguished by the relative band gap. 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. 1. In intrinsic semiconductors Fermi level is ammost in the middle of the band gap and hence at a particular temperature, conductivity will decrease exponentially with band gap. 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 intrinsic conductivity and intrinsic carrier concentrations are largely controlled by E g / k BT, the ratio of the band gap … 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. However, there are also many non-metallic conductors, including graphite, solutions of salts, and all plasmas. Recall from Chapter 6 that µ is the ratio of the carrier drift velocity to the electric field and has units of cm2/Volt-second. Because gold does not corrode, it is used for high-quality surface-to-surface contacts. However, some non-metallic materials are practical electrical conductors without being good thermal conductors. When a large number of atoms (1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. Wider gap materials (Si, GaAs, GaP, GaN, CdTe, CuIn, The density of carriers in the doped semiconductor (10, The activation energy for conduction is only 40–50 meV, so the conductivity does not change much with temperature (unlike in the intrinsic semiconductor). 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. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. This flow of charge (measured in amperes) is what is referred to as electric current. The intrinsic carrier concentration, ni, is equal to the number density of electrons or holes in an undoped semiconductor, where n = p = ni. Thus we expect the conductivity of pure semiconductors to be many orders of magnitude lower than those of metals. For solar cell applications, the semiconductor must have a wide band gap, and its electrical conductivity should be higher than that of the insulator. phosphorus in silicon). While insulating materials may be doped to become semiconductors, intrinsic semiconductors can also be doped, resulting in an extrinsic semiconductor. Many of the applications of semiconductors are related to band gaps: Color wheel showing the colors and wavelengths of emitted light. The defects facilitate the mobility of lithium ions, leading to greater Li-ion 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). These are also called “undoped semiconductors” or “i-type semiconductors. Auger electron spectrum of band gap illuminated ZnO powder sample as a function of electron energy taken at the same conditions as in fig. Other variations that add up to an octet configuration are also possible, such as CuIInIIISe2, which has the chalcopyrite structure, shown at the right. The band gap in At low temperature, no electron possesses sufficient energy to occupy the conduction band and thus no movement of charge is possible. This dynamic equilibrium is analogous to the dissociation-association equilibrium of H+ and OH- ions in water. This "law" is often violated in real materials, but nevertheless offers useful guidance for designing materials with specific band gaps. A very large band gap is indicative of an insulator--since it takes a great deal of energy for the electron to "jump" from the valence band to the conduction band, there will not likely be any conductivity. In this experiment, we will calculate the energy band gap in the intrinsic region and The impurities depend on the type of semiconductor. P-type Semiconductor: After the material has been doped with boron, an electron is missing from the structure, leaving a hole. 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. The separation between energy levels in a solid is comparable with the energy that electrons constantly exchange with phonons (atomic vibrations). This is exactly the right number of electrons to completely fill the valence band of the semiconductor. 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. 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). There are a number of places where we find semiconductors in the periodic table: A 2" wafer cut from a GaAs single crystal. File:Isolator-metal.svg - Wikipedia, the free encyclopedia. The band gap is a very important property of a semiconductor because it determines its color and conductivity. The result is that one electron is missing from one of the four covalent bonds normally part of the silicon lattice. The band gap is a very important property of a semiconductor because it determines its color and conductivity. 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. SrTiO3, Egap = 3.2 eV) do not absorb light in the visible part of the spectrum. Most familiar conductors are metallic. Although CeO 2 has a band gap of more than 3.0 eV, which is desirable for efficient charge separation, its electrical conductivity is much less than that of any other wide band gap semiconductor. In contrast to conductors, electrons in a semiconductor must obtain energy (e.g. Again, this process requires only 40–50 meV, and so at room temperature a large fraction of the holes introduced by boron doping exist in delocalized valence band states. Pure (undoped) semiconductors can conduct electricity when electrons are promoted, either by heat or light, from the valence band to the conduction band. It is clear that a plot of ( ) as a function of will yield a The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. The chalcopyrite structure is adopted by ABX2 octet semiconductors such as CuIInIIISe2 and CdIISnIVP2. Often, there is a linear relation between composition and band gap, which is referred to as Vegard's Law. Chemistry of semiconductor doping. In metallic conductors such as copper or aluminum, the movable charged particles are electrons. How does the band gap energy vary with composition? In semiconductors, the band gap is small, allowing electrons to populate the conduction band. Semiconductors and insulators are further distinguished by the relative band gap. When a conduction band electron drops down to recombine with a valence band hole, both are annihilated and energy is released. Copper is the most common material used for electrical wiring. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal latti… Some donors have fewer valence electrons than the host, such as alkali metals, which are donors in most solids. The most common example is atomic substitution in group-IV solids by group-V elements. This concept becomes more important in the context of semi-conductors and insulators. Since at low temperatures the number of electrons promoted across the band gap is small, the impurities would dominate any electrical conduc tion at low temperatures. (1) Going down a group in the periodic table, the gap decreases: Egap (eV): 5.4 1.1 0.7 0.0. Bonding in Elemental Solids 1.1. It is found that energy band gap of CdSe film is 1.67 eV. When a sufficiently large number of acceptor atoms are added, the holes greatly outnumber thermally excited electrons. In metallic conductors, such as copper or aluminum, the movable charged particles are electrons, though in other cases they can be ions or other positively charged species. Silver is the best conductor, but it is expensive. Light-Emitting Diodes (Note: Th… This atom will have three electrons and one hole surrounding a particular nucleus with four protons. Lightly and moderately doped semiconductors are referred to as extrinsic. Crucial to the conductivity method is whether or not or not there ar electrons inside the conductivity band. Metals: Weak Covalent Bonding 1.2. A conductor is a material which contains movable electric charges. to the band theory of solids, which is an outcome of quantum mechanics, semiconductors possess a band gap, i.e., there is a range of forbidden energy values for the electrons and holes. In the case of silicon, a trivalent atom is substituted into the crystal lattice. The entropy change for creating electron hole pairs is given by: $\Delta S^{o} = R ln (N_{V}) + R ln (N_{V}) = R ln (N_{C}N_{V})$. Table 1. 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. Bands and the Conductivity Properties of the Elements 2.1. The energy needed to ionize this electron – to allow it to move freely in the lattice - is only about 40–50 meV, which is not much larger the thermal energy (26 meV) at room temperature. The slope of the line in each case is -Egap/2k. 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. According to the mass action equation, if n = 1016, then p = 104 cm-3. from ionizing radiation) to cross the band gap and to reach the conduction band. Consequently, the difference in energy between them becomes very small. 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. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. It is commonly a metal. 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. Almost all applications of semiconductors involve controlled doping, which is the substitution of impurity atoms, into the lattice. Each anion (yellow) is coordinated by two cations of each type (blue and red). Sometimes it is not immediately obvious what kind of doping (n- or p-type) is induced by "messing up" a semiconductor crystal lattice. 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. 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. where e is the fundamental unit of charge, τ is the scattering time, and m is the effective mass of the charge carrier. Semiconductors are materials that have properties in between those of normal conductors and insulators; they are often produced by doping. 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