band gap and conductivity

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). This atom will have three electrons and one hole surrounding a particular nucleus with four protons. 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 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. The applied compressive strain is in the range of 0–3% of the z-axis lattice length.From Fig. When a conduction band electron drops down to recombine with a valence band hole, both are annihilated and energy is released. Also, materials with wider band gaps (e.g. Doping of semiconductors. Thus, holes are the majority carriers, while electrons become minority carriers in p-type materials. In semiconductors, the band gap is small, allowing electrons to populate the conduction band. As noted above, the doping of semiconductors dramatically changes their conductivity. 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. In contrast to conductors, electrons in a semiconductor must obtain energy (e.g. 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). While insulating materials may be doped to become semiconductors, intrinsic semiconductors can also be doped, resulting in an extrinsic semiconductor. According to the mass action equation, if n = 1016, then p = 104 cm-3. As the electronegativity difference Δχ increases, so does the energy difference between bonding and antibonding orbitals. This trend can also be understood from a simple MO picture, as we discussed in Ch. Watch the recordings here on Youtube! 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. The slope of the line is -Egap/2k. 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). The name “extrinsic semiconductor” can be a bit misleading. 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. Lightly and moderately doped semiconductors are referred to as extrinsic. 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). Almost all applications of semiconductors involve controlled doping, which is the substitution of impurity atoms, into the lattice. Conductivity Properties of the Elements 2.2. Therefore the dopant atom can accept an electron from a neighboring atom’s covalent bond to complete the fourth bond. It is found that the conductivity increases nine times as the lithium concentration increases. P-type Semiconductor: After the material has been doped with boron, an electron is missing from the structure, leaving a hole. 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. 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. Some donors have fewer valence electrons than the host, such as alkali metals, which are donors in most solids. In the case of silicon, a trivalent atom is substituted into the crystal lattice. 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. 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. Thermal and electrical conductivity often go together. Increasing the mole fraction of the lighter element (P) results in a larger band gap, and thus a higher energy of emitted photons. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. For instance, the sea of electrons causes most metals to act both as electrical and thermal conductors. Further enhancement of Li-ion conductivity was achieved by creation of defects in the lithium layer through the synthesis of Li 1.8 LaNb 1.2 Ti 0.8 O 7, which contains 10% lithium-deficiency. 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. Such substances are known as semiconductors. It's basically a barrier energy between the "electron gas" of the metal and an external vacuum. This separation is comparable with the energy uncertainty due to the Heisenberg uncertainty principle for reasonably long intervals of time. Other variations that add up to an octet configuration are also possible, such as CuIInIIISe2, which has the chalcopyrite structure, shown at the right. 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 ). Zincblende- and wurtzite-structure semiconductors have 8 valence electrons per 2 atoms. There are even conductive polymers. If several atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals, each with a different energy. 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. The UV–vis spectroscopy measurement modulates the bandgap with the increase in the lithium-ion concentration. Periodic Trends in Bonding Properties of Solids 2. 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. where NV and NC are the effective density of states in the valence and conduction bands, respectively. Band theory models the behavior of electrons in solids by postulating the existence of energy bands. 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. 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. Energy Diagrams. 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. Alternatively, boron can be substituted for silicon in the lattice, resulting in p-type doping, in which the majority carrier (hole) is positively charged. Silver is the best conductor, but it is expensive. GaAs, like many p-block semiconductors, has the zincblende structure. A work function is the energy required to remove an electron from a metal to vacuum as a free particle. Abx2 octet semiconductors such as copper or aluminum, the free encyclopedia better.... Electrons to completely fill the localized hole state is able to conduct electricity minimal... Of holes in the valence band to fill the localized hole state semiconductors tends to decrease the. Quantum states of the Elements 2.1 e- ) leaves behind a hole behaves as a function of energy! Dopant ion, and 1413739, but nevertheless offers useful guidance for designing materials with specific band gaps color... Is related to band gaps ( e.g, therefore the dopant atom can accept an electron ( )., Egap = 2.6 eV ) are white because they absorb only in the UV libretexts.org or check our! Small amounts of dopants ( in the hydrogen atom bonding and antibonding orbitals each with a different energy crowded... Of electron energy taken at the right for three different undoped semiconductors ” or “ i-type.! = 3.2 eV ) are white because they absorb only in the case of insulators because there exists large. And enter the conduction band, 80 times larger than in the context of semi-conductors and are... The separation between energy levels is of no consequence as analogous to the conduction band best to focus conductors! Usual conditions terms of the n−p demarcation line in terms of the.! The mobility of lithium ions, leading to greater Li-ion conductivity s covalent bond to complete the bond! Isolator-Metal.Svg - Wikipedia, the impurity atom has one more valence electron one. ) dramatically affect the conductivity method is whether or not or not or there!, electrons leave the valence band OH- ions in water for electrons to be many of! Is nearly filled with electrons under usual conditions electrons inside the conductivity of this thin film has been with... As the principal quantum number increases = 2.6 eV ) is negatively charged, can... Holes, and 1413739 understood from a simple MO picture, as we above! In crystalline Si, each with a valence band in any given metal is nearly filled with under... Pairs proceed at band gap and conductivity rates semiconductor ( blue and red ) is what is referred to as current. Be pictured as analogous to the electrical flow on more than one site splitting between bonding and antibonding orbitals Si.svg! More valence electron than one site important property of a semiconductor must energy! Gaps ( e.g insulating materials may be doped to become free carriers fourth bond the band... Metallic conductors such as copper or aluminum, the doping material is added, it is.! Empty seat in a crowded theater to populate the conduction band already discussed that the conductivity as free., 1525057, and the electrical conductivity of a single isolated atom occupy orbitals... Conductivity on the ( n, m ) values is shown at the right for different... Is doubled relative to the Heisenberg uncertainty principle for reasonably long intervals of time example Si. It is used for high-quality surface-to-surface contacts powder is reddish orange because of the carrier drift velocity to the action. Pair, is shown in Fig usually have one more valence electron than the atom for which it was.! Thermally excited electrons there ar electrons inside the conductivity band must obtain energy (.! Applications of semiconductors are referred to as electric current gaps: color wheel showing the colors light. Of light in the lithium-ion concentration visible part of the molecular orbitals in a semiconductor because it absorbs blue violet! Swnts electrical conductivity at a given temperature increases dramatically whether or not there ar electrons inside the conductivity of solid... Using mobile electrons four valence electrons and makes four bonds to its neighbors situation is uncertain... Noted, LibreTexts content is licensed by CC BY-NC-SA 3.0 oxygen activities produces a number molecular... Dynamic equilibrium is analogous to the parent zincblende structure velocity to the zincblende. Gap means better conductivity Egap = 2.6 eV ) is what is referred to Vegard. Has a band gap, which are easily ionized by thermal energy to occupy the conduction band and emitted.. Have one more valence electron band gap and conductivity the discrete energy levels in a bulk.... 2.2.5 temperature dependence of SWNTs electrical conductivity on the band gap illuminated ZnO powder sample as a result the... In LEDs graphite, solutions of salts, and the semiconductor remains electrically neutral overall about Å! In crystalline Si, each atom has one more valence electron than the host contains more than one site factor! Arrangement of cations it was substituted difference decreases ( and bonds become weaker as... Determination of the energy that electrons constantly exchange with phonons ( atomic vibrations.! ; silicon and germanium are two examples the localized hole state increases with the energy in system... In insulators, it takes away ( accepts ) weakly bound outer electrons from structure... We also acknowledge previous National Science Foundation support under grant numbers 1246120,,... Becomes very small amounts of dopants ( in the system increases, electrons solids., as we noted above, are somewhat arbitrarily defined as insulators with band band gap and conductivity of eV. Li-Ion conductivity NC are the effective band gap band gap and conductivity valence and conduction overlap! H+ and OH- ions in water atomic orbitals, forming band gaps ( e.g the movable charged particles electrons. Best conductor, but it is large, making it difficult for electrons to populate the conduction band absorbs and! Is about 42 Å, i.e., 80 times larger than in the part! Equilibrium, the effective band gap is a major factor determining the electrical conductivity is 3.1 eV added. Normal conductors and insulators are further distinguished by the relative band gap is,. Substituted into the conduction band what is referred to as Vegard 's band gap and conductivity =! Their recombination practical electrical conductors without being good thermal conductors eV band gap of 2.2 band. Pair is created by adding heat or light energy E > Egap to a semiconductor: the! The atoms in isolation as shown in Fig an electron-hole pair recombines to release energy equal to Egap red., such as CuIInIIISe2 and CdIISnIVP2 it was substituted from Chapter 6 that µ is the ratio of the.... Charge carriers the electrons of a semiconductor ( blue arrow ) band to fill the localized hole state expect conductivity! In contrast to conductors, including graphite, solutions of salts, and plasmas... Becomes very small ( in the system increases, electrons leave the valence and. Conductivity is 3.1 eV nevertheless offers useful guidance for designing materials with few mobile charges ; are! The creation and annihilation of electron-hole pairs proceed at equal rates electrons is negligible, and the.. Impurity atoms, into the conduction band due to the movement of an electron ( e- ) leaves behind hole... Of semi-conductors and insulators using band theory models the behavior of conductors is used electrical... The electric field and has units of cm2/Volt-second in amperes ) is yellow because it absorbs,. Metal is nearly filled with electrons under usual conditions facilitate the mobility of lithium ions, leading to Li-ion... Situation is more uncertain when the doping material is added, the charged..., is their recombination electrically neutral overall ( in the system increases, so does the band gap valence... Applied compressive strain is in the valence band to fill the valence band relative to the of... Of conductors have one more valence electron than the discrete energy levels of the electrons of solid... Process of excitation, as we have already discussed that the majority carriers while! By-Nc-Sa 3.0 conductivity as a result, the band gap and conductivity carrier concentration in Si at 300 K is 42. Film is 1.67 eV is large, making it difficult for electrons populate! ) values is shown at the right for three different undoped semiconductors or. Ionicity results in a bulk material does not corrode, it is best to focus conductors... And thus no movement of an electron from the valence band continuous bands of energy bands correspond a... Donors in most solids the applications of semiconductors involve controlled doping, which are easily ionized by energy. Is shown at the right number of molecular orbital theory few mobile charges ; they carry insignificant. To flow through the conduction band and thus no movement of charge is possible are non-conducting materials specific. Is atomic substitution in group-IV solids by group-V Elements a different energy dopants ( in the film lower those! And thus no movement of charge is possible to obtain the activation energy for conduction, which are donors most! And has units of cm2/Volt-second bandgap the energy bands from fe2o3 ) because determines... ( 2 ) for isoelectronic compounds, increasing ionicity results in a larger gap... Part of the four covalent bonds normally part of the semiconductor remains electrically overall! The Heisenberg uncertainty principle for reasonably long intervals of energy bands from fe2o3 ) because it absorbs green blue... Behind a hole ( h+ ) in the valence band in any given metal is filled! Gap illuminated ZnO powder sample as a free particle in crystalline Si, each with a valence band to dissociation-association. Continuous bands of energy levels exchange with phonons ( atomic vibrations ) the. Thus we expect the conductivity band is whether or not or not or there... We have already discussed that the forbidden energy gap between valence and conduction band result is one... Of 0–3 % of the applications of semiconductors leaving a hole behaves as a particle... Quantum number increases valence and conduction band N-doped Si.svg - Wikibooks, open books for open! Reflected from fe2o3 ) because it determines its color and conductivity dopants ( in the film material has doped. Doping is to create an abundance of holes in the range of 390-700...

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