The result is that one electron is missing from one of the four covalent bonds normally part of the silicon lattice. For example silicon, germanium. 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. The motion of holes in the lattice can be pictured as analogous to the movement of an empty seat in a crowded theater. Bands and the Conductivity Properties of the Elements 2.1. Temperature dependence of the carrier concentration. The band gap determined from the electronic component of the electrical conductivity is 3.1 eV. For solar cell applications, the semiconductor must have a wide band gap, and its electrical conductivity should be higher than that of the insulator. 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. 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). Similarly, CdS (Egap = 2.6 eV) is yellow because it absorbs blue and violet light. 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. It is found that the conductivity increases nine times as the lithium concentration increases. For more information contact us at or check out our status page at There are two types of extrinsic semiconductors that result from doping: atoms that have an extra electron (n-type for negative, from group V, such as phosphorus) and atoms that have one fewer electron (p-type for positive, from group III, such as boron). The most common example is atomic substitution in group-IV solids by group-V elements. The slope of the line is -Egap/2k. The chalcopyrite structure is adopted by ABX2 octet semiconductors such as CuIInIIISe2 and CdIISnIVP2. Like in case of conductors the two bands overlap and thus the electrons present in the lower energy band can easily move to the conduction band. Some donors have fewer valence electrons than the host, such as alkali metals, which are donors in most solids. N-type Semiconductor: After the material has been doped with phosphorus, an extra electron is present. where e is the fundamental unit of charge, τ is the scattering time, and m is the effective mass of the charge carrier. Semiconductors fall into two broad categories: In the classic crystalline semiconductors, electrons can have energies only within certain bands (ranges of energy levels). The separation between energy levels in a solid is comparable with the energy that electrons constantly exchange with phonons (atomic vibrations). Silver is the best conductor, but it is expensive. 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 conductivity of this thin film has been determined by I-V measurement using the electrometer. As the energy in the system increases, electrons leave the valence band and enter the conduction band. Electrical conductivity of non-metals is determined by the susceptibility of electrons to be excited from the valence band to the conduction band. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. This creates an excess of negative (n-type) electron charge carriers. It's basically a barrier energy between the "electron gas" of the metal and an external vacuum. 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. 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. These substitutions introduce extra electrons or holes, respectively, which are easily ionized by thermal energy to become free carriers. Apply the concept of band theory to explain the behavior of conductors. Also, materials with wider band gaps (e.g. Increasing the mole fraction of the lighter element (P) results in a larger band gap, and thus a higher energy of emitted photons. According to the mass action equation, if n = 1016, then p = 104 cm-3. In conductors (metals) there is zero band gap, therefore the valence and conduction bands overlap. Consequently, the difference in energy between them becomes very small. This allows for easier electron flow. Table 1. 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. 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 insulators, it is large, making it difficult for electrons to flow through the conduction band. 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. This flow of charge (measured in amperes) is what is referred to as electric current. For this reason a hole behaves as a positive charge. 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. The band gap is a very important property of a semiconductor because it determines its color and conductivity. 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. When a sufficiently large number of acceptor atoms are added, the holes greatly outnumber thermally excited electrons. The dependence of SWNTs electrical conductivity on the (n, m) values is shown in Table 1. 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. Pure (undoped) semiconductors can conduct electricity when electrons are promoted, either by heat or light, from the valence band to the conduction band. In semiconductors, the band gap is small, allowing electrons to populate 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. As we have already discussed that the forbidden energy gap between valence and conduction band is different for different material. This trend can be understood by recalling that Egap is related to the energy splitting between bonding and antibonding orbitals. In describing conductors using the concept of band theory, it is best to focus on conductors that conduct electricity using mobile electrons. n- and p-type doping. Taking an average of the electron and hole mobilities, and using n = p, we obtain, \[\mathbf{\sigma= \sigma_{o} e^{(\frac{-E_{gap}}{2kT})}}, \: where \: \sigma_{o} = 2(N_{C}N_{V})^{\frac{1}{2}}e\mu\]. This is exactly the right number of electrons to completely fill the valence band of the semiconductor. 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. Legal. Zincblende- and wurtzite-structure semiconductors have 8 valence electrons per 2 atoms. The entropy change for creating electron hole pairs is given by: \[\Delta S^{o} = R ln (N_{V}) + R ln (N_{V}) = R ln (N_{C}N_{V})\]. 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 conductivity (σ) is the product of the number density of carriers (n or p), their charge (e), and their mobility (µ). 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. 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. 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. A dopant can also be present on more than one site. File:N-doped Si.svg - Wikibooks, open books for an open world. Plots of ln(σ) vs. inverse temperature for intrinsic semiconductors Ge (Egap = 0.7 eV), Si (1.1 eV) and GaAs (1.4 eV). 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. Semiconductors, as we noted above, are somewhat arbitrarily defined as insulators with band gap energy < 3.0 eV (~290 kJ/mol). The band gap in 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. 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. 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. Doping atom usually have one more valence electron than one type of the host atoms. A work function is the energy required to remove an electron from a metal to vacuum as a free particle. The crystal is n-doped, meaning that the majority carrier (electron) is negatively charged. If several atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals, each with a different energy. The unit cell is doubled relative to the parent zincblende structure because of the ordered arrangement of cations. In both cases, the effective band gap is substantially decreased, and the electrical conductivity at a given temperature increases dramatically. 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 … However, the valence band is completely filled in case of insulators because there exists a large band gap between valence and conduction band. The slope of the line in each case is -Egap/2k. Si has a slight preference for the Ga site, however, resulting in n-type doping. For example, the intrinsic carrier concentration in Si at 300 K is about 1010 cm-3. It is observed that the conductivity increases with the increase of temperature. 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). 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 kind of plot, which resembles an Arrhenius plot, is shown at the right for three different undoped semiconductors. 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). P-type Semiconductor: After the material has been doped with boron, an electron is missing from the structure, leaving a hole. Insulators are non-conducting materials with few mobile charges; they carry only insignificant electric currents. It is clear that a plot of ( ) as a function of will yield a There are a number of places where we find semiconductors in the periodic table: A 2" wafer cut from a GaAs single crystal. This atom will have three electrons and one hole surrounding a particular nucleus with four protons. 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 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). Chemistry of semiconductor doping. 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. A band gap is an energy range in a solid where no electron states can exist due to the quantization of energy. The name “extrinsic semiconductor” can be a bit misleading. Almost all applications of semiconductors involve controlled doping, which is the substitution of impurity atoms, into the lattice. Energy Diagrams. If you are talking about photoconductivity, then smaller energy band gap means better conductivity. Such substances are known as semiconductors. The opposite process of excitation, which creates an electron-hole pair, is their recombination. In contrast to conductors, electrons in a semiconductor must obtain energy (e.g. n- and p-type doping of semiconductors involves substitution of electron donor atoms (light orange) or acceptor atoms (blue) into the lattice. Often, there is a linear relation between composition and band gap, which is referred to as Vegard's Law. 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. Sometimes it is not immediately obvious what kind of doping (n- or p-type) is induced by "messing up" a semiconductor crystal lattice. CC licensed content, Specific attribution,,,,,,,,,,,,, Conductivity Properties of the Elements 2.2. The mass action equilibrium for electrons and holes also applies to doped semiconductors, so we can write: \[n \times p = n_{i}^{2} = 10^{20} cm^{-6} \: at \: 300K\]. When a large number of atoms (1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. Wide band gap semiconductors such as TiO2 (3.0 eV) are white because they absorb only in the UV. In crystalline Si, each atom has four valence electrons and makes four bonds to its neighbors. This release of energy is responsible for the emission of light in LEDs. How does the band gap energy vary with composition? (1) Going down a group in the periodic table, the gap decreases: Egap (eV): 5.4 1.1 0.7 0.0. The obtained data allow the determination of the n−p demarcation line in terms of temperature and oxygen activities. Bands may also be viewed as the large-scale limit of molecular orbital theory. As a result, the separation between energy levels is of no consequence. This difference decreases (and bonds become weaker) as the principal quantum number increases. phosphorus in silicon). A conductor is a material that is able to conduct electricity with minimal impedance to the electrical flow. 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 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. Periodic Trends in Bonding Properties of Solids 2. 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. GaAs, like many p-block semiconductors, has the zincblende structure. Have questions or comments? 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. 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). The applied compressive strain is in the range of 0–3% of the z-axis lattice length.From Fig. 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. 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). \[n_{i}^{2} = N_{C}N_{V} e^{({- \Delta H^{o}}{RT})}\], Since the volume change is negligible, \(\Delta H^{o} \approx \Delta E^{o}\), and therefore \(\frac {\Delta H^{o}}{R} \approx \frac{E_{gap}}{k}\), from which we obtain, \[n_{i}^{2} = N_{C}N_{V} e^{(\frac{-E_{gap}}{kT})}\], \[\mathbf{n= p = n_{i} = (N_{C}N_{V})^{\frac{1}{2}} e^{(\frac{-E_{gap}}{2kT})}}\]. When the doping material is added, it takes away (accepts) weakly bound outer electrons from the semiconductor atoms. At low temperature, no electron possesses sufficient energy to occupy the conduction band and thus no movement of charge is possible. 6 that the mobility μ is given by: \[\mu = \frac{v_{drift}}{E} = \frac{e\tau}{m}\]. 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. 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. This is due to the increase of grain size and removal of defects, which are present in the film. 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. The band gap is a major factor determining the electrical conductivity of a solid. 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. Visible light covers the range of approximately 390-700 nm, or 1.8-3.1 eV. These combinations include 4-4 (Si, Ge, SiC,…), 3-5 (GaAs, AlSb, InP,…), 2-6 (CdSe, HgTe, ZnO,…), and 1-7 (AgCl, CuBr,…) semiconductors. 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. Watch the recordings here on Youtube! 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). It is commonly a metal. When the gap is larger, the number of electrons is negligible, and the substance is an insulator. 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. The situation is more uncertain when the host contains more than one type of atom. When a conduction band electron drops down to recombine with a valence band hole, both are annihilated and energy is released. 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. The UV–vis spectroscopy measurement modulates the bandgap with the increase in the lithium-ion concentration. The band gap is a very important property of a semiconductor because it determines its color and conductivity. In metallic conductors such as copper or aluminum, the movable charged particles are electrons.